distributed system designers

Abstract: The Simultaneous Message Passing (SMP) model provides a fundamental framework for comparing classical and quantum communication. For two players, Gavinsky et al. (STOC 2006) established a separation underlying the incomparability of shared randomness and quantum communication: \textsc{Index Coordination} needs $O(\log n)$ public-coin bits but $Ω(n^{1/3})$ bounded-error qubits. In this work, we establish a multiparty exponential separation through $\operatorname{IC}_{k,n}$, a natural $k$-party generalization of \textsc{Index Coordination}. Public-coin protocols solve it unambiguously with maximum message length $O(\log n)$ bits. In contrast, quantum SMP protocols without shared entanglement or public coins require maximum message length $Ω(n^{1-1/k})$ qubits in the unambiguous regime and $Ω(n^{(k-1)/(k+1)})$ qubits in the bounded-error regime. A classical private-coin protocol matches the unambiguous bound, so quantum communication provides no asymptotic advantage over private randomness in this regime. For fixed error parameters, all constants are independent of $k$, establishing the exponential separation for every integer-valued function $k=k(n)\ge2$, without restricting its growth. Both quantum lower bounds become $Ω(n)$ when $k\ge c\log n$ for any fixed $c>0$, matching the full-input protocol and yielding tight linear complexity in both regimes. Our results demonstrate that quantum superposition cannot efficiently simulate the coordination afforded by public randomness, extending this separation to arbitrary $k$. To bound success probabilities for multiparty product states, we prove an exact factorization theorem for unambiguous quantum state identification, which may be of independent mathematical interest.

Abstract: We propose a variable and behavior-based node-specific proof-of-work (PoW) model for a directed acyclic graph (DAG)-based distributed ledger technology (DLT) network to mitigate decentralized network congestion control. Network congestion control for centralized communication systems is an established field of study, with detailed and continuous research being done on the subject. However, attention to congestion control in decentralized networks is relatively recent and underexplored, especially with DLT, such as blockchain and DAG-based networks. For the DLT networks, the network congestion is caused by factors such as transaction spamming, an increase in the user base, and the launch of new tokens. We focus on the congestion caused by the spamming of transactions within the blockchain and DAG-based DLT network. Based on the network throughput of transactions per second and consensus procedure, the DAG-based DLT needs to control network spamming more than the blockchain network. The PoW model within the DLT consensus framework is a limited deterrent against spamming. Our model provides equal opportunities for all stakeholders regardless of their computational resources. It prevents and penalizes any node that attempts to spam or dominate the network with more than the prescribed number of transactions. Since the system nodes compete to issue transactions with finite network resources, we display the system behavior through a non-cooperative game. Further, we show that our model enforces prescribed behavior amongst the nodes through the proof of the existence of Nash equilibrium in the game.

Abstract: We show that one-way one-round quantum LOCAL algorithms cannot $4$-color directed cycles with high probability, even with unbounded local computation and quantum message length. This is the first lower bound in the high-probability quantum LOCAL setting that goes beyond the non-signaling and bounded-dependence models, exploiting the structure of distributed quantum algorithms. Our proof connects distributed quantum computing with noncommutative extremal combinatorics by identifying local collision probabilities with the weighted multiplicative energy of matrix-space decompositions. We obtain our lower bound by proving a dimension-independent weighted stability theorem for a directed noncommutative analogue of Mantel's theorem.