quantum communication engineers

Abstract: Single-photon avalanche diodes (SPADs) are essential components of quantum communication receivers. In practical systems, some SPADs exhibit intrinsic step-like changes in dark-count rate (DCR), commonly referred to as random telegraph signal (RTS) noise. Similar RTS-like variations, however, can also arise from stray light, temperature-dependent threshold crossings, cable disturbances, electrical interference, and other readout artifacts. Distinguishing intrinsic RTS from these artifacts is important because they originate from different mechanisms and require different corrective actions. We present a self-referenced diagnostic that primarily uses the low-to-high afterpulse-yield ratio R, together with complementary checks based on DCR-state reproducibility, cross-channel behavior, and event timing. Four commercial SPAD modules were monitored in darkness for more than 920 h. Three exhibited intrinsic DCR switching of 44.59%, 19.33%, and 2.77%, with corresponding R values of $0.9996\pm0.0027$, $1.0050\pm0.0023$, and $1.0027\pm0.0043$, all consistent with unity. Controlled experiments reproduced temperature-related threshold crossings, light leakage, cable-contact artifacts, and artificial electrical injection. These artifacts produced distinct correlation and timing signatures: temperature-related threshold crossings gave intermediate pair-survival responses, cable disturbances and electrical injection generated sub-dead-time events, while light leakage produced simultaneous cross-channel switching and nonreproducible DCR levels. Combining R with orthogonal timing and DCR-based checks provides a practical self-referenced diagnostic framework for distinguishing intrinsic RTS from non-intrinsic artifacts using primarily time-tagged dark-count data.

Abstract: How much entanglement can two distant laboratories share when their connection is noisy? We relate this question to deciding which of two quantum hypotheses is present. Our one-shot bounds apply to entanglement generation over a quantum channel and to one-way entanglement distillation from a shared state. We use Cheng's trace inequality to bound the infidelity of a Petz decoder in terms of a binary hypothesis testing cost. Applying the inequality before averaging over codes reduces the error analysis to computing a second moment of random subspaces. The proof covers every integer target dimension and treats rank-deficient states explicitly. A corollary expresses the achievable entanglement through hypothesis-testing coherent information, with a single logarithmic error slack and exact integer rounding. We also prove an error-preserving conversion from entanglement generation codes to entanglement transmission codes: the target dimension decreases by only a constant factor at fixed error, and the decoder is the original decoder followed by local processing. Consequently, for both entanglement generation and entanglement transmission, arbitrary pure reference-input states yield the same coherent-information rate, second-order Gaussian correction at the original error tolerance, and explicit achievable logarithmic remainder. For commuting testing hypotheses, the logarithmic remainder improves to a constant. These results give a direct route from binary distinguishability to explicit recovery guarantees and finite-resource quantum communication rates.

Abstract: Quantum key distribution (QKD), whose security is derived from quantum mechanics rather than computational assumptions, is moving into standardization and commercial deployment. Yet its security guarantees rest on technically delicate proofs checked by hand. Formal verification closes this gap, establishing a two-factor assurance: unconditional security from physical principles, and machine-checked proofs against reasoning errors. We present FVQKD, a Rocq library for machine-checking QKD security proofs. Its first result is a complete, end-to-end machine-checked proof of composable, finite-key security for BB84. The mechanization reconstructs the complete proof infrastructure from first principles, including the smooth entropy framework, the entropic uncertainty relation, and the Quantum Leftover Hash Lemma. It uncovers necessary side conditions that the published argument leaves unstated, one of which reveals a missing proof branch, and it grounds the information-theoretic bound in a formal semantics of protocol execution, which the pen-and-paper analysis lacks. The proof is entirely admit-free, relying only on the Rocq kernel and standard foundational axioms. To our knowledge, this is the first end-to-end formal verification of a QKD security proof. Built on MathComp, MathComp-Analysis, and CoqQ, the development provides quantum-information infrastructure designed for reuse across broader QKD variants and quantum cryptography applications.

Abstract: We prove that the randomized communication complexity of Vector-in-Subspace in $\mathbb R^n$ with error at most $1/3$ is $Θ(\sqrt n)$. Alice holds a unit vector $u$ and Bob holds an $n/2$-dimensional subspace $H$; they must distinguish $u\in H$ from $u\in H^\perp$. An exact one-way quantum protocol uses $O(\log n)$ qubits, making the problem a geometric example of an exponential quantum advantage over interactive classical communication. Our lower bound matches Raz's $O(\sqrt n)$ upper bound, improves the $Ω(n^{1/3})$ lower bound of Klartag and Regev, and removes the total-rank restriction in Grupel's $Ω(\sqrt n)$ result. The proof establishes a Gaussian moment bound over complete rectangle partitions. A complex Gaussian representation yields a vanishing even moment whose cancellation is preserved when averaging over the partition. We control the signed conditional moments around a real center by decomposing conditional Gaussian measures into fixed coordinates and sub-Gaussian components. Combining this estimate with spherical harmonic analysis gives the communication lower bound.

Abstract: We exhibit a bipartite language with a poly-logarithmic quantum communication protocol and polynomial Merlin-Arthur communication complexity.

Abstract: Private simultaneous quantum messages (PSQM) provide a minimal model of noninteractive secure multiparty quantum computation, yet their communication complexity for concrete functions remains poorly understood. We show that familiar total functions already exhibit both genuine quantum advantages and strong structural limitations. For three-party equality on $n$-bit inputs, which determines whether the players' $n$-bit strings are identical, we construct an entanglement-assisted protocol with asymptotic communication $(1.633\ldots)n$ qubits, whereas every perfectly correct protocol without prior entanglement requires at least $3n$ qubits. For three-bit majority, one shared GHZ state and one transmitted qubit per player suffice for perfect correctness and perfect privacy, reducing the communication from the optimal classical cost of six bits to three qubits. Three-bit AND behaves differently. No perfectly correct and perfectly private protocol exists when the players share an arbitrary three-qubit state, apply arbitrary local unitary encodings, and transmit one qubit each. However, increasing the local dimension overcomes this obstruction: one shared three-qutrit GHZ state and one transmitted qutrit per player yield a one-shot protocol with total communication $3\log_2 3$. Together with the six-bit classical lower bound, this gives a strict quantum communication advantage. More generally, for every $k\geq 3$, we construct a perfectly correct and perfectly private one-shot protocol for $k$-bit AND using one qudit of dimension at most $k$ per player, and hence at most $k\log_2 k$ qubits in total.

Abstract: We determine the finite-horizon identification limits of a \(d\)-dimensional memory when the control interface is restricted to four shared, time-homogeneous generators. A writer encodes a message by applying a prefix word to a common root state. The verifier then applies a candidate-dependent query word followed by a shared terminal binary test, with each word of length at most \(T\). For fixed error tolerances \(λ_2>0\) and \(λ_1+λ_2<1\), the optimal identification sizes satisfy \(\ln N_{\mathsf Q,4}=Θ_{λ_1,λ_2}(\min\{d^2,T\})\) for arbitrary CPTP generators and \(\ln N_{\mathsf S,4}=Θ_{λ_1,λ_2}(\min\{d,T\})\) for stochastic maps. Four unitary letters and four permutation letters attain these respective bounds, showing that a four-letter reversible alphabet reaches the static code-size orders in optimal quadratic and linear word length. In the fully dimension-limited regime, this yields \(\ln N_{\mathsf Q,4}=Θ(d^2)\) versus \(\ln N_{\mathsf S,4}=Θ(d)\), establishing a quadratic quantum--classical separation in logarithmic code size. Low-overlap Grassmann and agreement-code packings supply the orbit endpoints, while exact inverse query words match each encoded state to its designated test. At the sharp boundary \(λ_2=0\), \(0\leqλ_1<1\), all four model classes satisfy \(\ln N=Θ(\min\{\ln d,T\})\). Thus any fixed positive false-acceptance tolerance activates the metric-packing regime, whereas zero false acceptance imposes an exclusive-witness constraint and yields the logarithmic-dimension boundary.

Abstract: We study zero-error communication and exact simulation of quantum channels assisted by quantum no-signalling correlations. For a channel with Kraus operator space $K$, we introduce a semidefinite programming parameter $Γ(K)$ that is exactly multiplicative under tensor products and upper-bounds $Θ_{\rm NS}(K)$, where $\log_2Θ_{\rm NS}(K)=C_{0,\rm NS}(K)$ and $C_{0,\rm NS}(K)$ denotes the asymptotic quantum no-signalling-assisted zero-error capacity. Among known upper bounds on $Θ_{\rm NS}$ given by semidefinite programs, $Γ$ is the tightest. We also prove that the previously introduced simulation lower bound $Σ^{-}(K)$ is exactly multiplicative and satisfies $Θ_{\rm NS}(K)\leqΓ(K)\leqΣ^{-}(K)\leqΓ(K)^2$. Using this multiplicativity, we show that neither $S_{0,\rm NS}(K)=\log_2Σ^{-}(K)$ nor its regularized extension $S_{0,\rm NS}(K)=\lim\nolimits_{n\to\infty}n^{-1}\log_2Σ^{-}(K^{\otimes n})$ holds in general. This answers an open question about the asymptotic simulation cost $S_{0,\rm NS}(K)$. For classical-quantum channels, we obtain sharp bounds. If $r$ is the effective output dimension, then $Θ_{\rm NS}\leqΓ\leq(1+r^{1/2})Θ_{\rm NS}/2$ and $Γ\leqΣ^{-}\leq(1+r^{1/2})Γ/2$. If $k$ is the minimum rank of the output support projections, then $Σ^{-}/Θ_{\rm NS}\leq[(1+r^{1/2})/(1+k^{1/2})]^2$, and this bound is sharp for every $1\leq k\leq r$. Thus, we obtain the sharp bound $S_{0,\rm NS}-C_{0,\rm NS}\leq2\log_2[(1+r^{1/2})/(1+k^{1/2})]$.

Abstract: Loss and noise limit the use of light to distribute entanglement, transmit quantum information, and establish secret keys. Gaussian states have a compact description in terms of means and covariance matrices, but their entanglement still requires global optimization. We develop a framework for computing Gaussian-restricted versions of the relative entropy of entanglement and Rains entanglement. An integral representation reveals a convex geometry under matrix geometric means and reduces Gaussian Rains entanglement to relative entropy minimized over Gaussian states with positive partial transpose. We obtain unique optimal reference states and additivity for independent Gaussian input states. Our convex-majorization algorithm has an explicit geometric convergence rate, uniform in the faithful regularization parameter and valid for pure input states. Controlled numerical integration and approximate convex subproblem solutions give a bit-complexity bound that is polynomial in accuracy bits for each fixed rational input covariance matrix, with explicit dependence on covariance size. These calculations bound extractable entanglement and, through the relative entropy of entanglement, extractable secret key. Teleportation simulation, energy allocation, and a convex optimization of passive-basis loss cores give bounds on quantum and private communication under an input-energy constraint, allowing arbitrary two-way classically assisted protocols. Two- and three-mode examples compare the bounds with achievable rates, including matching pure-loss benchmarks. Finally, we separate the Gaussian-restricted quantities from their unrestricted counterparts and give a photon-number truncation method with controlled error for computing the latter.

Abstract: We study a strong form of genuine multipartite nonlocality (GMNL), where an $n$-partite scenario admits a quantum strategy generating outcomes belonging to a restricted set with certainty, whereas every strategy built from nonclassical resources shared among at most $k<n$ parties fails this criterion with positive probability. This generalizes what is referred to as strong contextuality/nonlocality, or pseudotelepathy, beyond ruling out local models. For the simplest five-party Bell scenario of two binary-outcome measurement settings per party, we use the inflation technique to demonstrate that a game with a perfect quantum strategy witnesses a robust separation from models built from bipartite resources under local operations and shared randomness (LOSR), establishing the behavior is LOSR-GMNL. We provide broader context for this result by investigating its simulability with resources shared among three or four parties under different resource models and alternative definitions of GMNL. A central open question is whether $n$-party quantum resources can achieve such a separation from models built from $(n-1)$-party resources, for $n\ge 3$. We make progress here by constructing a family of robustly LOSR-GMNL games with $ε$-optimal quantum strategies experimentally indistinguishable in the limit from true probability-one-winning strategies for any desired level of precision.

Abstract: The security of a secret sharing protocol is compromised if one or more dishonest participants can reconstruct the secret by deviating from the prescribed protocol, particularly when such malicious behavior remains undetected. Semi-Quantum Secret Sharing (SQSS) is a variant of secret sharing in which the participants possess only classical capabilities, such as preparing and measuring qubits in the computational ($Z$) basis, while a quantum-capable third party assists the dealer in generating and distributing quantum shares of a classical secret. The limited quantum capabilities of the participants in SQSS protocols may introduce vulnerabilities to collusion attacks, enabling an assisting quantum third party, in collaboration with a dishonest classical participant, to jointly recover the secret even without detection. In this work, we propose a novel SQSS protocol that eliminates this vulnerability and achieves information-theoretic security against collusion attacks. We further prove that the proposed protocol is secure against a broad class of external and internal attacks. Finally, a comparative analysis demonstrates that our construction advances existing SQSS protocols by simultaneously optimizing qubit efficiency, involves a classical dealer, and resilience against DCNA attacks using basic Bell states.

Abstract: In quantum reading, classical messages are encoded in sequences of quantum channels and recovered by probing the channels and processing their outputs. We study the reading capacity of a finite family of finite-dimensional channels under an average constraint on the probing energy, allowing arbitrary adaptive operations between channel uses. Using an input-dependent chain rule for the Belavkin-Staszewski relative entropy, we derive a converse bound expressed as an optimization involving channel Choi operators and the operator relative entropy. This formulation admits semidefinite approximations and reduces, without an energy constraint, to a channel information radius. To obtain achievable rates, we construct bilinear semidefinite lower approximations to a standard non-adaptive reading bound. Alternating optimization produces feasible probe states and encoding distributions, whose Holevo information gives a directly evaluable achievable rate. For jointly classical-quantum channels, we derive a separate converse based on the Umegaki relative entropy. Without an energy constraint, this converse matches a non-adaptive achievable rate, recovering a recent result of Pascual Abraldes and Winter: non-adaptive protocols suffice to achieve the unconstrained reading capacity of jointly classical-quantum channels.

Abstract: We study collective state preparation and channel encoding in fermionic systems under parity superselection and composition governed by the canonical anticommutation relations. For a two-mode Gaussian state $τ$, we obtain the exact entanglement of formation, $E_{\mathrm F}^{\mathrm{phys}}(τ^{\otimes m})=\lceil m/2\rceil\log2$ for every $m\geq1$. Two copies have the same formation value as one, violating additivity and strong superadditivity, while regularization halves the single-copy value. For an associated Gaussian channel, we determine the minimum output entropy and Holevo information at every blocklength and prove nonadditivity of both. Together, these results give exact answers to the fermionic counterparts of the four additivity questions associated with Shor and Hastings. One physical use carries no classical information, whereas two uses transmit one bit perfectly. The unassisted classical and zero-error classical capacities both equal one half bit per mode. A sharp finite-block bound gives a strong converse: the decoding success probability vanishes at every rate above capacity. These optimizations cover all physical pure-state decompositions and channel inputs, with Gaussian ensembles and classical codes attaining the optima. The formation and minimum output entropy formulas hold for every Rényi order $α\in(0,\infty]$. We also determine the unassisted quantum and zero-error quantum capacities, both equal to one half logical qubit per mode, and prove a strong converse: entanglement fidelity vanishes at every rate above capacity. For a noisy Gaussian family, we determine the one- and two-copy formation values and prove strict nonadditivity at full rank. For $τ$, Bell violation under local parity-preserving measurements first appears at three copies.

Abstract: In the general probabilistic model of information theory, the signaling dimension of a given communication protocol (or, equivalently, of its state space) is the smallest possible complexity of a classical communication protocol capable of perfectly simulating the given one in terms of input-output correlations. The signaling dimensions of three-, four-, and five-dimensional cross-polytopes have been known to be 3. We give an upper and a lower bound for signaling dimensions of higher dimensional cross-polytopes.

Abstract: We develop entanglement-of-formation potentials for feedback-assisted classical communication and one-way randomness distillation. For a finite-dimensional quantum channel without initial shared entanglement, an exact amortization theorem bounds the increase of message information plus entanglement remaining across the communicating laboratories. This proves a classical-feedback capacity bound using a mixed-convex-roof expression previously studied by Winter and Yang in the context of potential capacities. We determine the capacity of flagged mixtures of noiseless and entanglement-breaking channels, improve a published depolarizing-channel converse, and evaluate the new bound exactly for the amplitude damping channel. A state analogue gives a finite-blocklength upper bound on the net shared randomness obtainable with one-way classical communication. Amplitude-damping Choi states provide exact benchmarks, while a full-rank generalized amplitude-damping Choi state demonstrates a useful improvement where we do not evaluate the operational rate exactly. We also distinguish one-way from two-way randomness distillation: a two-round weak-measurement protocol strictly exceeds the exact one-way rate of every nontrivial qubit isotropic state. The protocol preserves quantum side information during its first decoding and extracts additional randomness in the reverse direction. This shows why the one-way state potential is not a general two-way converse. Together, these results establish a common entanglement-based approach to sharper communication and randomness bounds, while revealing how retained quantum correlations enable two-way distillation to surpass one-way limits.

Abstract: We study quantum-state oblivious transfer over the quantum erasure channel under information-theoretic security guarantees. Specifically, Alice holds two quantum systems, Bob wishes to recover one of them, and the parties have access to independent channel uses and authenticated public classical communication, with no initial shared entanglement. We consider both honest-but-curious and malicious behavior. We establish finite-blocklength converse and achievability bounds, which match in the honest-but-curious setting. The malicious setting construction combines interactive hashing with tests of whether Bob received selected channel outputs, and distributes each input across several qubits so that erasures conceal an entire input from a dishonest receiver, even when the inputs are entangled with an external reference. We also derive fixed-error asymptotic expansions and show that both malicious and honest-but-curious settings have the same capacity.

Abstract: Recent examples have shown that zero private capacity need not imply antidegradability and that two channels with zero private capacity can nevertheless transmit private information together. Existing entropic channel orders compare what a receiver and its environment can learn and thereby bound capacities. We connect these orders to the recent constructions through binary estimation, whose minimum mean-square error is governed by measured $χ^2$ divergence. A new integral representation shows how measured $χ^2$ on a qubit extension recovers quantum $χ^2$. It lets us pass from complete measured-$χ^2$ ordering to complete quantum-$χ^2$, relative-entropy, and less-noisy ordering. Zhu and Wang used a signed lift to show that their qutrit channel has zero private capacity. We show that Hermitian-smoothed measured-$χ^2$ ordering characterizes when such lifts exist, even with a quantum reference. Environmental dominance in binary estimation at every blocklength yields a finite-code reliability--secrecy bound. These results explain why complete comparison prevents activation with antidegradable helpers whereas regularized comparison alone does not. Building on that qutrit example, we establish this stability for a range of noisy Werner--Holevo channels, determine sharp private-capacity and antidegradability thresholds, and compute exact complementary capacities in a nondegradable range. By contrast, we extend Pauli half-erasure activation to all $1/2\le p<1$ and establish the same range for a new four-level family. Reference-assisted measured-$χ^2$ witnesses show why these activating constructions lack complete comparison.

Abstract: We prove that the von Neumann entanglement of purification is nonadditive. For two-qubit Werner states $W(f)$ with singlet weight $1/64\le f\le1/4$, we show that canonical purification is globally optimal: its entanglement, also known as reflected entropy, gives the exact entanglement of purification. In contrast, the regularized entanglement of purification lies strictly below the reflected entropy for $0<f<f_\ast$, where $f_\ast\approx0.017$. Together, these results establish nonadditivity throughout $1/64\le f<f_\ast$. Our canonical-optimality proof generalizes the proof in [1], which established Rényi nonadditivity for $0\leα<1$ using classical two-qubit states. We thus resolve the additivity question at $α=1$. Remarkably, nonadditivity is again witnessed by separable states and no entanglement in the underlying states is required.

Abstract: For classical--quantum wiretap channels with a transitive covariant input action, both output ensembles admit a description as unitary group orbits of fixed seed states. We use this structure to construct finite-block preprocessing schemes whose private information is an entropy difference evaluated at two distributions related by group convolution. Applying the construction to product groups allows correlations across any fixed number of channel uses. We give a sufficient condition for the associated uniform-input bound to equal the single-use private information. Constant-composition channel codes and universal$_2$ hashing achieve the resulting rates, with trace-distance leakage controlled by sandwiched Rényi information. For uniform outer randomization, the representation structure reduces the comparison-state optimization to Eve's invariant states. For the hybrid binary channel considered by Tikku, Berta and Renes, numerical optimization at three and four uses gives rates above our numerical estimate of the optimized noisy-repetition benchmark wherever that estimate is positive on the tested grid. The improvement comes from noise distributions beyond the family of independent physical flips and a symmetric logical flip. We also prove nonadditivity at an explicit channel parameter using a two-use encoder, an analytic single-use converse, and certified entropy bounds. Finally, we relate the hybrid model to binary phase-shift keying with a fixed receiver measurement.

Abstract: Universal channel coding enables communication without a complete description of the channel. For classical channels, universal codes can attain both capacity and the optimal high-rate reliability. We show that this compatibility fails for classical-quantum channels in general; that is, the optimal reliability in the channel-aware scenario is not always achievable with universal coding due to the ignorance of the unitary rotation of the output system. We exhibit a family of classical-quantum channels for which one cannot achieve the channel-aware optimal reliability by a fixed coding scheme. We further derive a converse bound on the reliability for unitary-invariant decoders, a natural assumption for the universal coding scheme, that can be strictly smaller than the optimal channel-aware error exponent. Conversely, we construct a channel-independent encoder-decoder pair and establish a universally achievable bound on the reliability that matches this converse bound in the high-rate regime, thereby characterizing the optimal universal reliability. Specifically, the channel-aware and universal exponents are governed by the Petz and sandwiched Rényi divergences, respectively. These divergences coincide for commuting outputs but differ for noncommuting ones, explaining why universality preserves optimal reliability classically but can reduce it quantumly. Our results showcase the fundamental reliability cost of performing the classical-quantum channel coding task universally.

Abstract: Device-independent conference key agreement (DI-CKA) lets a group of parties establish a shared secret key from untrusted quantum devices, with security certified by non-locality. Existing DI-CKA protocols are each built around a single Bell inequality, typically a multiparty variant of the CHSH game. DI-QKD protocols, in contrast, have been built from a much richer landscape of non-local games, and it has remained unclear how to carry this landscape over to the conference setting. We introduce $\textit{Parity-$G$ games}$, which extend any two-player game $G$ to $N$ players, for every $N$, provided $G$ has an optimal strategy in which one player measures Pauli observables. The extension preserves the quantum and classical values of $G$, and the security of the resulting $N$-party protocol follows from an analysis of the two-player game alone. Our framework recovers the Parity-CHSH game of Ribeiro, Murta and Wehner (Phys. Rev. A, 2018) as a special case. Applied to the Mermin--Peres Magic Square Game, it yields a new $N$-player pseudo-telepathy game, the $\textit{Parity Magic Square Game}$, which ideal devices win in every round. We use it to construct the $\textit{first}$ DI-CKA protocol based on a pseudo-telepathy game. We prove the protocol secure against coherent attacks. It produces up to two key bits per round, and at low noise its key rate exceeds that of the DI-CKA protocol based on the Parity-CHSH game.

Abstract: We give the first exponential quantum advantage in the general interactive three-party Numbers-on-Forehead (NOF) model for a decision problem. Previous separations hold only for restricted protocols like one-way communication for a relation. We construct an explicit partial Boolean function, the Interleaved Unitary Product problem, that requires only $O(\log n)$ NOF quantum communication but $\widetildeΩ(n^{1/32})$ randomized communication. This function builds on the two-party unitary product problem of Arunachalam, Girish, and Lifshitz (TQC 2024). The main technical obstacle is that discrepancy, the standard lower-bound method for NOF, also lower-bounds quantum communication. We instead develop a regularity-based argument for randomized NOF lower bounds, building on the approach of Kelley, Lovett, and Meka and adapting the regularity decomposition of Abboud, Fischer, Kelley, Lovett, and Meka (STOC 2024) to cylinder intersections. Combined with matrix-product estimates of Arunachalam, Girish, and Lifshitz, this yields our randomized lower bound.

Abstract: We present a universal entanglement distillation protocol that asymptotically achieves the distillable entanglement of any unknown bipartite state in a fixed finite dimension. That is, its ebit yield attains every rate below the optimum that would be available if the state were known, with vanishing trace-distance error. Our approach combines tomography by local operations and classical communication with an adaptive distillation routine, using a local robustness lemma to control finite-sample estimation errors. We also characterize worst-case distillation from a family of states: the optimal uniform rate is the minimum distillable entanglement on the family's closure. These results show that ignorance of the state need not incur an asymptotic rate penalty.

Abstract: The bosonic quantum entropy power inequality bounds the entropy of a beam-splitter output in terms of the input entropies. We determine its complete equality class among independent inputs of finite mean photon number: for any number of modes and any transmissivity strictly between zero and one, equality in either the linear or the exponential form holds if and only if the inputs are Gaussian with the same covariance matrix, allowing arbitrary displacements. The main step shows that equality for one output forces the two outputs to be independent: a thermal auxiliary converts equality into preservation of mutual information by a fixed noisy channel, and a two-outcome instrument shows that preservation of mutual information requires a product state with the reference. The quantum Darmois--Skitovich theorem then gives Gaussianity, while a central-limit argument reduces exponential equality to linear equality.

Abstract: We study the noise threshold for positive quantum capacity for the qubit depolarizing channel. We explore analytically the action of the qubit depolarizing channel on the symmetric subspaces of the input qubits, in the limit of asymptotically many uses of the channel. We observe the emergence of a bosonic Gaussian channel. Furthermore, the codes previously developed for the depolarizing channel can be translated to codes for the emergent Gaussian channel, and it is easier to further optimize these codes for the simpler emergent Gaussian channel. Translating these codes back to the depolarizing channel leads to extremely good input states for the coherent information of the depolarizing channel producing new lower bounds on the noise threshold for positive capacity. In addition to improved lower bounds on the threshold, this newly found link between depolarizing noise and Gaussian channels offers a novel perspective contributing to our understanding of these symmetric codes.

Abstract: Quantum information complexity (QIC), introduced by Touchette [Touchette, STOC 2015], has been shown to be one of the most powerful methods for proving quantum communication complexity and has also been shown to be equal to amortized quantum communication complexity. Unfortunately, QIC is generally hard to analyze because it is a sum of quantum conditional mutual information terms, which are difficult to estimate. In this work, we introduce a new variational approach, the information potential, for analyzing QIC and proving quantum communication lower bounds inspired by the resolvent representation for quantum relative entropy. This approach connects the QIC of individual messages to a quadratic form, making it more amenable and thus enables us to bound the cumulative positive increments of the potential throughout an interactive quantum protocol by its QIC. Lower bounds on the growth of the potential therefore translate into lower bounds on both QIC and quantum communication complexity. As an application, we give an optimal $Ω(1/r)$ lower bound on the QIC of the two-bit $\mathsf{AND}$ function as well as an optimal $Ω(n/r)$ lower bound on the quantum communication complexity of $r$-round Set-Disjointness, answering an open problem in~[Braverman, Garg, Ko, Mao, Touchette FOCS 2015]. Moreover, we further prove a direct-sum theorem for bounded-round quantum communication complexity of Set Disjointness. With the tight bound on the QIC of $\mathsf{AND}$ function, we further establish a nearly tight tradeoff for the asymmetric quantum communication complexity of $\mathsf{Set} \mathsf{Disjointness}$: $(q_A+1)(q_B+1)=Ω(n)$, where $q_A$ and $q_B$ denote the total numbers of qubits sent by Alice and Bob, respectively.

Abstract: In this paper, we study the conditions under which covert communication at positive rates is feasible over discrete memoryless classical, classical-quantum, and quantum channels. For classical point-to-point channels, we show that if the dimension of the channel input probability simplex exceeds that of the channel output probability simplex, equivalently, if the input alphabet has larger cardinality than the output alphabet, then positive covert rates are achievable for certain classes of Discrete Memoryless Channels (DMCs). We further show that allowing the innocent symbol (i.e., the symbol transmitted in the no-communication mode) to be chosen appropriately can enlarge the class of DMCs for which positive covert rates are achievable. We also study covert communication over classical Multiple-Access Channels (MACs), where the additional transmitter effectively enlarges the set of available channel input pairs, and we show that the conditions required to satisfy the covertness constraint are less restrictive for MACs than for point-to-point channels. We extend these results to classical-quantum DMCs by showing that if the dimension of the input probability simplex exceeds the affine dimension of the set of output states that can be induced at the channel output, then positive covert rates are achievable for certain classes of classical-quantum DMCs. Finally, for quantum channels, we show that if the innocent state (i.e., the state transmitted in the no-communication mode) is mixed, then the covertness constraint can always be satisfied by a non-trivial input ensemble. Consequently, positive covert rates are achievable whenever the legitimate receiver can distinguish at least two states in a suitable such ensemble.

Abstract: We prove an exponential strong converse for the unassisted private capacity of every finite-dimensional degradable quantum channel. We use a single error criterion: the infidelity between the actual message-estimate-environment state and an ideal state consisting of uniformly distributed, perfectly correlated messages that are independent of the environment. At every rate strictly above the channel's maximum coherent information, the optimized fidelity to this ideal state decays exponentially in the number of channel uses. The same bound holds when the ideal environment state is fixed to the actual environment marginal. The proof applies to arbitrary mixed-state encoders and arbitrary collective decoders. Its main operator ingredient is an overlap bound for privacy tests: two receiver placements with a common subsystem of dimension $d_C$ have overlap at most $d_C/M$, where $M$ is the key size, independently of both shield dimensions. We combine this bound with the signed averaging construction presented in arXiv:2608.01308 and a single-filter reduction to symmetric states. A Gaussian filter replaces the common receiver subsystem by a system of controlled dimension from which the original correlations can be approximately recovered using quantum side information. The filter preserves exact exchange symmetry, and a uniform smooth-entropy estimate bounds its output dimension for arbitrary correlated channel inputs. We also obtain an exponential strong converse at zero for antidegradable channels under the same joint criterion and, consequently, for the private capacity of the quantum erasure channel throughout its parameter range.

Abstract: We introduce lower bounds on the minimum distance of one-generator quasi-cyclic codes of arbitrary index, obtained by puncturing and shortening the code at the level of its blocks. For balanced codes, these bounds form a nondecreasing chain whose first term is the Jensen bound. We apply these bounds to conduct a computer search and obtain many Hermitian LCD codes with good parameters. Among them there are six codes of length at most 30 which improve the corresponding lower bounds of Araya and Harada. These codes further give maximal-entanglement entanglement-assisted quantum codes, which we compare with the parameters currently recorded in the literature.

Abstract: We study interactive multiprover games and many-round protocols in which the communication between the verifier and the provers is quantum. Parallel repetition is known to suppress soundness error of classical two-prover games arbitrarily close to zero, as shown by Raz (STOC '95), even with quantum strategies as shown by Yuen (ICALP '16), and Bavarian, Vidick and Yuen (STOC '17). Yet, we show that quantum communication can have the opposite, unexpected effect. Specifically, we exhibit a one-round quantum game and two-round $\mathsf{QMIP}$ protocols whose local (unentangled) value is strictly less than one for a single instance, yet equals one under $n$-fold parallel repetition for every $n \geq 2$. The key is that parallel repetition not only imposes additional winning conditions but also supplies additional quantum resources as entanglement in the exchanged states can be exploited jointly across copies. Our multiround examples build on superactivation of zero-error capacities of quantum channels. To establish this connection, we introduce quantum games and interactive protocols which capture the one-shot zero-error classical and quantum capacities, both with and without entanglement assistance. Our constructions use quantum-state verification and a teleportation-based reduction from two rounds to one. In contrast, when shared entanglement is allowed, we show that parallel repetition cannot increase the entangled value when at most $3$ messages are exchanged, consistent with classical results of Bellare, Impagliazzo and Naor (FOCS '97), and that of single-prover systems by Kitaev and Watrous (STOC '00). Combining this monotonicity with our quantum game-channel correspondence, we show that entanglement-assisted zero-error classical and quantum capacities cannot be superactivated.

Abstract: We prove that the regularized, stabilized sandwiched Rényi divergence of finite-dimensional quantum channels converges to their regularized relative entropy as the Rényi order tends to one. The key tool is the channel hockey-stick divergence: Gour's Stinespring approximation bound and a Schatten norm estimate amplify an asymptotic bound below one into exponential decay at higher threshold rates. For channel pairs with finite max-relative entropy, known operational connections then give exponential strong converses for parallel and adaptive discrimination, a sharp zero--one testing law, and the subchannel asymptotic equipartition property.

Abstract: We study the transmission of two independent confidential classical messages over a quantum broadcast channel, one for each receiver. Each message must remain secret from the other receiver, including when that receiver knows its own message. For classical inputs and quantum outputs, we establish the classical Marton-type inner bound under average reliability and conditional strong secrecy. The encoder selects pairs of codewords from independently generated codebooks using normalized likelihood weights. We prove reliability through a change-of-distribution argument. Our main technical result is a bipartite classical-quantum resolvability theorem that accounts for the dependence created by pair selection and establishes secrecy for the same encoder. We also obtain a multi-letter capacity characterization and extend it to arbitrary quantum inputs under secrecy against the other receiver, together with the Stinespring environment. We recover confidential capacity regions for deterministic classical and degraded classical-quantum channels, with an explicit evaluation for the classical Blackwell channel. For coherent isometric extensions of injective deterministic classical broadcast channels, we show that the confidential classical capacity region equals that of the corresponding classical channel. We then compare confidential classical communication with quantum transmission. For the coherent isometric extension of the Blackwell channel, we determine the unassisted quantum-capacity region and show that some achievable confidential classical rate pairs lie outside it. The Platypus channel provides another example of this separation.

Abstract: We construct an explicit family of finite-dimensional quantum channels for which the optimal classical communication rate achievable with product-state codewords and collective decoding tends to zero, while rates achievable using entanglement only within pairs of channel inputs grow without bound. Our construction combines deterministic qudit Clifford unitaries with a binary measurement and classical feedforward, providing a derandomization to Hastings' probabilistic construction. The key ingredient is a careful design of measurement and feedforward process that yields the required one-copy and two-copy output entropy bounds from moment estimates alone, without requiring strong convergence of the underlying unitary family.

Abstract: The direct static capacity region of a bipartite quantum state describes its asymptotic conversion into classical communication, quantum communication, and entanglement, with all communication directed from Alice to Bob. This paper gives a unified entropic converse for this region. The proof treats generated and consumed resources simultaneously and derives all three information inequalities for one local instrument. Its main ingredients are no-signalling, the chain rule, strong subadditivity, and continuity of conditional entropy. A supporting-hyperplane characterization leads to the static capacity formula, which is helpful in determining single-letterization of the capacity region. For a pure state of entanglement entropy $h$ subjected to erasure with probability $p$, the complete region is the convex hull of $0$ and $(0,-ph,(1-p)h)$, plus the unit-resource cone. This statement holds for arbitrary collective instruments by using subset-entropy inequalities related to earlier methods used for the dynamic capacity region of the erasure channel. Complete characterizations also hold for symmetrically extendible states and locally flagged pure-state mixtures. For maximally correlated states, the optimization over local instruments admits an exact matrix formulation and an additive outer bound. An explicit qubit example shows that a nonorthogonal discarded quantum memory can outperform every efficient instrument and every instrument with conditionally commuting discarded states. For states obtained by qubit dephasing of Schmidt-aligned pure states, an exact threshold characterizes when the static capacity formula vanishes, at every blocklength and after regularization. Full single-letter characterizations for general Hadamard states and for the remaining trade-offs for dephased states remain open, with sufficient additivity conditions identified.

Abstract: Locally recoverable codes (LRCs) combine global error correction with the ability to repair a small number of erased coordinates by accessing only a limited number of other coordinates. Motivated by their quantum counterparts, we construct several families of optimal cyclic $(r,δ)$-LRCs that are Euclidean or Hermitian dual-containing. In the Euclidean case, we obtain four families of optimal dual-containing cyclic $(r,δ)$-LRCs over $\mathbb{F}_q$ with a range of minimum distances extending beyond the local distance $δ$. In the Hermitian case, we derive analogous families over $\mathbb{F}_{q^2}$ that are Hermitian dual-containing, when $(r+δ-1)\mid(q^2-1)$. In addition, we develop a distinct construction for the case $(r+δ-1)\mid(q^2+1)$ using symmetric defining sets and odd $δ$, which yields optimal codes with minimum distances $\ell+2$, $δ+2$, $2δ-2$, and $2δ$. The Euclidean Calderbank-Shor-Steane (CSS) and Hermitian stabilizer constructions then give corresponding quantum cyclic $(r,δ)$-LRCs over~$\mathbb{F}_q$. Further, the resulting stabilizer codes are pure; they meet the relevant quantum Singleton-type bound, and are therefore \textit{optimal}. We also provide a comparison with previous works, highlighting the parameter regimes and minimum distance ranges covered by our results that are not attained by existing constructions. Explicit examples illustrate the constructions and verify the dual-containment and purity conditions.

Abstract: In quantum networks, nodes are connected via sharing of Einstein-Podolsky-Rosen (EPR) pairs, ideally with high fidelity and high rate. However, the fidelity of EPR pairs degrades due to imperfect generation and decoherence errors. Entanglement Distillation is a method that increases the fidelity but operates probabilistically and may destroy all involved EPR pairs upon failure. This failure reduces available EPR pairs for application use, thereby decreasing the service rate. Quantum Error Correction (QEC) is another mechanism to protect EPR pairs against error by forming what we term as Coding-Enhanced Memory (CEM). While effective, CEM requires extra time and resources to form the code, which also reduces the service rate. Existing methods often use static combinations of distillation and CEM, ignoring demand variations. This results in a low service rate without significant fidelity gain. Limited resources together with this rate-fidelity tradeoff make it essential to schedule when to run distillation, form CEM, or serve requests. We propose ReFINE, a demand-aware preemptive scheduler that based on application requirements either serves an available EPR pair immediately or preserves it in CEM. This selective use of CEM, only when needed, enables a better balance for rate-fidelity tradeoff than always using CEM. Between request arrivals, ReFINE either schedules distilling EPR pairs or forming CEM to protect distilled pairs, following one of the three priority policies: ReFINE-D (Distillation-First) first generates EPR pairs for distillation and then forms the CEM, prioritizing service rate. ReFINE-M (Memory-First) first forms the CEM, then generates the EPR pairs for distillation, prioritizing fidelity. ReFINE-C (Concurrent) performs both distillation and CEM formation concurrently, balancing between fidelity and service rate.

Abstract: Quantum communication underpins secure information processing and scalable quantum networks. In particular, remote state preparation (RSP) enables efficient quantum state transfer, but accurately estimating target states under complex noise remains challenging. Here, we propose a Transformer-based Quantum State Characterizer (TQSC) model for noisy RSP experiments. Our model reconstructs experimentally prepared pure and mixed photonic polarization states from noisy measurements in complex scattering environments, while its attention patterns provide physically grounded insights into correlations among the measured observables. The method achieves a mean estimator-target fidelity exceeding 99.999% under complex scattering and dynamic Gaussian noise, while its robustness and generalization are further examined using Qiskit-simulated Bloch-ball states.Furthermore, in a practical MNIST image transmission task with held-out states, the decoded bit error rate is reduced from 50.34% to zero after TQSC post-processing. The TQSC model enables accurate tomographic characterization under dynamic noise and provides physically grounded post-hoc insights, holding promise for intelligent quantum information processing applications.

Abstract: We establish unbounded two-use Holevo additivity gaps in finite dimensions. For each sufficiently large fixed integer $K$ and all sufficiently large $n$, we construct channels $T_n$ with output dimension $K^n$, input dimension $\exp(Θ_K(n^2))$, and \[ χ(T_n^{\otimes2})-2χ(T_n) \ge n\left[\frac{\log_2K}{K}-2\log_2(1+9/K)\right]-O(1/n). \] The gap is linear in output qubits, with an explicit quadratic input-qubit cost and an explicit threshold on $n$. We also obtain channels whose single-use Holevo quantity tends to zero while their two-use Holevo information, and hence classical capacity, diverges. The channels arise from structured tensor products of the complementary mixed-unitary channels used in Collins's free-probabilistic proof. We establish minimum-output-entropy gaps by combining Collins--Youn's product-group Haagerup inequality with Bordenave--Collins's quantitative strong-convergence estimates

Abstract: For a collection of states indexed by $[n]={1,\ldots,n}$, let $F(H)$ denote the optimal unnormalized minimum discrimination error for each nonempty subfamily $H\subseteq[n]$. We call $F$ the discrimination profile and characterize exactly which profiles can arise in a general probabilistic theory (GPT). For fixed $n$, the GPT region $\mathfrak{G}_n$ is a bounded rational polytope, giving a hierarchy $\mathfrak{C}_n\subseteq\mathfrak{Q}_n\subseteq\mathfrak{G}_n$ of classical, quantum, and GPT profiles, analogous to the local--quantum--no-signalling hierarchy in Bell theory. For $n=3$ we determine the classical and GPT polytopes explicitly. Within $\mathfrak{G}_3$, the classical region is characterized by $β:=F(123)-F(12)-F(13)-F(23)\le0$, while the GPT maximum is $1$. For qubit triples, the maximal value is attained by the trine, $β_{\mathrm{tr}}=3\sqrt3/2-2$, and we prove the dimension-independent quantum bound $β_{\mathrm Q}\le2/3$, with a slight further improvement. Hence $0=β_{\mathrm C}<3\sqrt3/2-2\leβ_{\mathrm Q}\le2/3<1=β_{\mathrm{GPT}}$. We conjecture $β_{\mathrm Q}=β_{\mathrm{tr}}$ and prove this for arbitrary pure-state triples, together with further supporting evidence. For arbitrary $n$, every classical facet admitting a GPT violation already admits a quantum violation in dimension at most $3$. A four-state qubit example shows that quantum success profiles need not be submodular, unlike for $n=3$. Finally, we exhibit a four-dimensional quantum triple whose discrete profile is classical for all subfamilies but becomes nonclassical when unequal priors are allowed.

Abstract: The generalised quantum Stein's lemma is a key result in quantum hypothesis testing, and connects this fundamental primitive of quantum information processing with quantum resource manipulation, a task that is central for technological applications. Prior works have proved this statement in the idealised setting of independent and identically distributed (i.i.d.) sequences of quantum states, and recent extensions consider also sources that are 'close' to i.i.d., according to the strict notion put forth by Mazzola, Sutter, and Renner. For several applications, however, one would need to consider yet more general sources. We establish a version of the generalised quantum Stein's lemma that is conceptually much simpler and general, as it applies to any source that is asymptotically close to an i.i.d. state with respect to the normalised quantum Wasserstein distance of order 1. As an immediate consequence, we solve the Stein exponent of a scenario where the null hypothesis is arbitrarily varying, expressing it in terms of i.i.d. Stein exponents corresponding to arbitrary states in the convex hull of the null hypothesis base set.

Abstract: We refine Gavinsky's framework (arXiv:2608.18784) for exponential separations between quantum and randomized communication complexity of total functions and obtain larger separations: polylogarithmic quantum communication versus $\tildeΩ(\sqrt n)$ randomized communication with two quantum messages, and versus $Ω(n^{1-\varepsilon})$ for every fixed $0<\varepsilon<1$ with more quantum messages.

Abstract: This paper reports the proof of a strong converse for the unconstrained quantum capacity of the pure-loss bosonic channel. At every fixed rate above capacity, the entanglement-generation fidelity of every code is bounded by a constant times the reciprocal of the number of channel uses. The bound holds without an energy constraint and for arbitrary encoded states, including states correlated across all input modes, and arbitrary joint decoders. The proof combines quantum Chebyshev and hockey-stick testing inequalities with a uniform relative-entropy-variance bound for the balanced pure-loss channel, corresponding to transmissivity $η=1/2$. The variance bound follows by expressing the balanced beam splitter in bright and dark modes: the dark modes are exactly in vacuum, and any state orthogonal to that vacuum contains at least one dark photon. For general transmissivity, dilating the degrading attenuator reduces the problem to this balanced-channel setting and bounds the decoder test by precisely the factor that produces the known quantum-capacity threshold. The resulting argument establishes the strong converse at the unconstrained quantum capacity for every pure-loss bosonic channel.

Abstract: The connection between coding theory and combinatorial $t$-designs is an important research topic at the intersection of coding theory and combinatorics. Let $q=p^m$, where $p$ is an odd prime and $m\geq 2$. In this paper, we investigate a class of linear codes $\mathcal{C}$ over $\mathbb{F}_{q^2}$ and their connection with combinatorial $3$-designs. By analyzing the relevant structural properties of $\mathcal{C}$ and $\mathcal{C}^{\perp}$, we show that the supports of the codewords of every nonzero weight in $\mathcal{C}$ and {the supports of the codewords of weight $4$ in $\mathcal{C}^{\perp}$} form $3$-designs. We further investigate a class of nonlinear codes $\mathcal{C}_2$ associated with $\mathcal{C}$, and prove that the supports of the codewords of every nonzero Hamming weight in $\mathcal{C}_2$ also form $3$-designs. These results identify further classes of linear and nonlinear codes whose codewords support combinatorial $3$-designs. In particular, the nonlinear case provides additional examples of codes supporting $3$-designs, a topic for which relatively few results are currently available. As applications, we construct from $\mathcal{C}^{\perp}$ an entanglement-assisted quantum error-correcting code with parameters $[[q+1,q-3,4;4]]_q$. We also prove that $\mathcal{C}$ is an all-symbol locally repairable code with locality $3$. Furthermore, we show that the code $\mathcal{C}$ {meets the Singleton-type bound for locally repairable codes} and hence is optimal in some cases.

Abstract: The classical capacity of a quantum channel is the highest rate at which classical information can be transmitted with vanishing error. Although the capacities of many fundamental quantum channels have been established, the capacity of the generalized amplitude-damping channel remains an open problem in quantum Shannon theory. In this work, we revisit a converse bound introduced by Brandão et al. [Phys. Rev. Lett. 106, 230502 (2011)], which upper-bounds the classical capacity in terms of a correlation measure. For the generalized amplitude-damping channel, we derive a relaxation of this measure that makes the converse bound efficiently computable. Numerical comparisons demonstrate that our bound is pretty tight in general and nearly coincides with the Holevo information at nonzero temperatures, significantly improving upon existing bounds across the entire parameter range.

Abstract: Squashed entanglement is an additive bipartite entanglement measure. For a state $ρ_{AB}$, it is defined as the infimum of all conditional mutual information $I(A:B\mid E)$ evaluated on extensions $ρ_{ABE}$. It was unresolved whether there is a bound on the dimension of the conditioning system, $E$, needed for this optimization. We show that no such cardinality bound is possible. Explicitly, we find that the squashed entanglement for a partially dephased Bell pair on two qubits cannot be achieved for any finite dimensional extension $E$. A crucial ingredient of this proof is a direct sum step, which in a sense, symmetrizes two purifying systems while keeping the conditional mutual information unchanged and the coherence no worse.

Abstract: We present two results derived from the sharp log-Sobolev inequality for the uniform measure on a complete graph which concern the von Neumann entropy and the Entanglement of Formation of a state of finite and infinite-dimensional quantum systems. The first result is a sharp Lipschitz lower semicontinuity bound for the von Neumann entropy at any mixed state $ρ$ with uniform positive spectrum (i.e. a state proportional to a projector) w.r.t. the fidelity deficit: the inequality $\,S(ρ)-S(σ)\leq C_ρ(1-F(ρ,σ))\,$ valid for any state $σ$, where $C_ρ$ is a constant depending on the rank of $ρ$. The second result is a sharp Lipschitz lower semicontinuity bound for the Entanglement of Formation at any pure state $ρ$ with uniform positive spectrum of marginal states: the inequality $\,E_F(ρ)-E_F(σ)\leq \frac{1}{2}\,C_ρ\|ρ-σ\|_1\,$ valid for any state $σ$, where $C_ρ$ is a constant depending on the Schmidt rank of $ρ$. In both cases the optimal constant $C_ρ$ is equal to the optimal constant $K_{d}$ in the log-Sobolev inequality for the complete graph with $d$ vertices: in the first case $d=\mathrm{rank}ρ$, in the second one $d=\mathrm{rank}ρ_A=\mathrm{rank}ρ_B$. The authors are grateful to GPT 5.6 for valuable discussion and technical help in preparing this note.

Abstract: Private communication over a noisy quantum channel requires reliable transmission to the receiver and secrecy from the environment. Whether two channels with zero private capacity can jointly enable private communication is a longstanding open problem in quantum information theory. Here we resolve this problem by exhibiting a four-level channel and a qubit erasure channel with half erasure probability, each with zero private capacity, whose joint use achieves more than 0.0001903 private bits per product use. The encoding gives the receiver a linear information gain with at most quadratic environmental leakage, enabling privacy through a fixed joint measurement and classical coding. This superactivation, impossible for independent classical memoryless wiretap channels, shows that a channel's private capacity alone does not determine its value for secure communication. The initial activation example was identified through interactions with large language models, and the result has been formalized in Lean 4.

Abstract: Quantum measurements are conventionally optimized to maximize the average of a utility that depends on the true state and on the measurement outcome. However, when the outcome of the measurement is used as an action within a larger decision-making system, the average utility does not capture the risk of poor outcomes. This letter addresses the design of quantum measurements that maximize a risk-averse objective given by the optimized certainty equivalent (OCE), a family of criteria that includes the average utility and the conditional value at risk (CVaR) as special cases. For a piecewise linear gain function, defining the OCE, thus including the CVaR, the problem is shown to reduce to a finite number of semidefinite programs, for which a dual formulation is derived. For the discrimination of two states, a closed-form solution is obtained that takes the form of a Helstrom measurement. Numerical results show that the optimized measurement improves the lower tail of the utility distribution at a moderate cost in average utility.

Abstract: Computing the optimal success probability for transmitting classical messages through a single use of a quantum channel is NP-hard, even for two messages. An existing semidefinite programming hierarchy based on symmetric extensions provides convergent upper bounds with an a priori error estimate that decays as the inverse square root of the extension level. In this work, we construct a Hermitian sum-of-squares hierarchy for an arbitrary number of messages and prove quadratic convergence in its level. The error bound is proportional to the advantage over random guessing. Our approach combines state-discrimination duality with positive polynomial kernels on products of spheres to construct feasible polynomial dual certificates. For binary messages, the resulting bounds give a multiplicative approximation from above of the trace-norm contraction coefficient.

Abstract: We introduce a framework for distributed quantum inference under communication constraints. In our model, $m$ distributed nodes each receive one copy of an unknown $d$-dimensional quantum state $ρ$, before communicating via a constrained one-way communication channel with a central node, which aims to infer some property of $ρ$. This framework generalizes the classical distributed inference framework introduced by Acharya, Canonne, and Tyagi [COLT 2019], by allowing quantum resources such as quantum communication and shared entanglement. Within this setting, we focus on the fundamental problem of quantum state certification: Given a complete description of some state $σ$, decide whether $ρ=σ$ or $\|ρ-σ\|_1\geq ε$. Additionally, we focus on the case of limited communication between distributed nodes and the central node: we assume each communication channel is limited to only $n_c$ bits and $n_q$ qubits with $n_c + n_q \leq \log d$. When all nodes can make use of a shared source of randomness, we show that the copy complexity of distributed state certification is $Θ(\frac{d^2}{2^{n_q} 2^{n_c/2}ε^2})$. We further demonstrate that shared randomness is necessary to achieve the above complexity, by proving an $Ω(\frac{d^3}{4^{n_q} 2^{n_c} ε^2})$ lower bound in the $\textit{private-coin}$ setting. Moreover, we develop a private-coin algorithm that matches this bound up to a $\sqrt{\log d}$ factor, showing this complexity is near-optimal. Together, our work establishes a general framework for distributed quantum inference with communication constraints and characterizes the complexity of distributed state certification with limited communication.

Abstract: The main goal of steganography is to transmit hidden messages in legitimate-looking communication messages. Phase-domain information hiding, however, has not been fully explored for quantum systems. This work introduces a finite-dimensional Quantum Hilbert Transform (QHT) as a unitary phase operator based on the Quantum Fourier Transform. Using this construction, we develop a QHT-based quantum steganography scheme that embeds classical bits as weak signed phase perturbations of quantum cover states. Bob recovers the hidden message through binary state discrimination, block aggregation, and classical error-correcting decoding.

Abstract: Let $R_2 = \mathbb{F}_{p^m} + u\mathbb{F}_{p^m}$ ($u^2 = 0$), where $p$ is an odd prime and $m, s \in \mathbb{N}$. For $p \equiv 3, 5 \pmod 7$ with $\gcd(m, 6) = 1$, the cyclotomic polynomial $Φ_7(x)$ is irreducible over $\mathbb{F}_{p^m}$. This yields a direct sum decomposition $C = C_1 \oplus C_2$ for any cyclic code $C$ of length $7p^s$ over $R_2$, where $C_1$ has length $p^s$ and $C_2$ is a $7$-cyclotomic code of length $6p^s$. We classify $7$-cyclotomic codes into four disjoint generator-based types and calculate exact cardinalities using residue and torsion subcodes. Furthermore, explicit generators for the Euclidean dual codes $C^\perp$ are determined. As operational applications of these classified codes, we construct new families of quantum stabilizer codes via the CSS framework and establish parameter criteria for linear codes with complementary duals (LCD codes).