quantum error correction teams

Abstract: We study the variation of hull dimensions of symplectic linear codes under equivalence transformations preserving the symplectic distance. For a symplectic linear code $C$, we introduce an even-valued invariant $Δ(C)$, which depends only on the equivalence class of $C$. This invariant can be expressed as the generic rank of an associated space of alternating matrices and, equivalently, as twice a corresponding matroid matching number. If $C$ has dimension $k$, we prove that the minimum symplectic hull dimension among all codes equivalent to $C$ is $k-Δ(C)$. Consequently, $C$ is equivalent to a symplectic LCD code if and only if $Δ(C)=k$. We further show that every symplectic MDS code of even dimension is monomially equivalent to a symplectic LCD code. For a symplectic self-orthogonal code $C$, we determine all attainable hull dimensions: for every integer $r$ with $0\le r\le Δ(C)/2$, there exists a monomially equivalent code whose symplectic hull has dimension $k-2r$. We also refine a standard form for the generator matrix of a symplectic self-orthogonal code and derive the corresponding parity-check matrix and the Gram matrix of the dual code. In the self-dual case, we characterize $Δ(C)$ through minors of an associated symmetric matrix. Furthermore, we relate hull variation to graph matchings, establish a bound for $Δ(C)$, and give graph constructions producing symplectic self-dual MDS, optimal, and best-known codes.

Abstract: Routing unknown quantum information across distributed communication networks requires autonomous, measurement-free mechanisms to prevent wave-function collapse. Szegedy quantum walks provide a mechanism for spatial state transport. The conventional walks on unweighted graphs suffer from severe back-reflection, spatial dispersion, and channel crosstalk. In this paper, we introduce a deterministic topological quantum routing architecture based on coined Szegedy quantum walks on edge-duplicated signed graphs. By treating edge signs as localized phase shifts within a balanced coin reflection, we enforce an exact zero back-scattering condition across routing nodes. We demonstrate deterministic Perfect State Transfer (PST) with unit fidelity at exact arrival times across fundamental archetypes, including the signed dumbbell switch $D_{2m,0,2n}$ and scalable glued binary trees. Furthermore, we analyse routing performance under realistic open-system amplitude and phase damping noise channels.

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.