Entanglement improves coordination in distributed systems

TL;DR

This work addresses coordination in latency-constrained distributed routing by introducing entanglement as a resource to improve decisions when only local observations are available. It develops a two-server FCFS model with a convex baseline throughput $T(t)$, derives a $w$-threshold routing policy at fixed splitting probability, and maps the problem to a weighted non-local game. The main contributions show that classical threshold strategies are certifiably optimal at fixed $p$, while entanglement-enabled strategies can strictly outperform classical bounds over a nontrivial range of $p$, yielding Pareto improvements in waiting time and baseline throughput. The analysis, including queueing theory, non-local games, and numerical certification, demonstrates a concrete near-term application pathway for quantum networks in distributed scheduling and load balancing.

Abstract

Coordination in distributed systems is often hampered by communication latency, which degrades performance. Quantum entanglement offers fundamentally stronger correlations than classically achievable without communication. Crucially, these correlations manifest instantaneously upon measurement, irrespective of the physical distance separating the systems. We investigate the application of shared entanglement to a dual-work optimization problem in a distributed system comprising two servers. The system must process both a continuously available, preemptible baseline task and incoming customer requests arriving in pairs. System performance is characterized by the trade-off between baseline task throughput and customer waiting time. We present a rigorous analytical model demonstrating that when the baseline task throughput function is strictly convex, rewarding longer uninterrupted processing periods, entanglement-assisted routing strategies achieve Pareto-superior performance compared to optimal communication-free classical strategies. We prove this advantage through queueing-theoretic analysis, non-local game formulation, and computational certification of classical bounds. Our results identify distributed scheduling and coordination as a novel application domain for near-term entanglement-based quantum networks.

Figures (3)

• Figure 1: Distributed system studied in this work. Two servers, depicted by squares, handle two distinct types of work. On the right, a baseline task that is preemptible and always available. On the left, customer requests that dynamically arrive at the system via the routers, depicted as circles. The servers are endowed with queues of unlimited size in which customers wait. The routers may share entanglement with each other, which they can use to better coordinate their routing decisions. Entanglement is depicted here by wavy lines connecting the two routers.
• Figure 2: The routing problem as a non-local game. Routers A and B receive inputs (service times $X_1$, $X_2$) and produce outputs ($o_A, o_B \in \{+1,-1\}$) without communication. The product $o_A \cdot o_B$ determines whether the customer pair is split across servers or bunched to the same server.
• Figure 3: Waiting time gap $\Delta W_q = (A^* - A)/2$ versus normalized throughput for quantum and classical strategies. Classical values are certified upper bounds; quantum values are achieved payoffs. Bottom axis: normalized throughput $\mathcal{T}/[\phi_{\max}(1-\rho)]$; top axis: corresponding splitting probability $p$. System parameters: $\lambda = 0.8$, $\mu = 1$, $\alpha = 0.5$.

Theorems & Definitions (57)

• Definition 1: Pareto Optimality
• Theorem 1: Pareto Optimality
• Definition 2: Non-local game
• Lemma 1: Payoff $\leftrightarrow$ Waiting Time Gap
• Theorem 2: Quantum Advantage in Routing
• proof
• Theorem 3: Classical Strategies are Threshold Strategies
• Theorem 4: Quantum Advantage Region
• Proposition 1: Load Balancing
• Theorem 5: Optimal threshold policy