Quantum Nonlocality under Latency Constraints

TL;DR

This paper explores how latency constraints affect quantum nonlocal correlations, extending Bell inequalities to scenarios with partial communication, and introduces a framework for analyzing physically realizable correlations under these conditions.

Contribution

It introduces latency-constrained games, extending nonlocal games to include partial communication, and provides a framework for understanding quantum correlations with latency constraints.

Findings

Extended Bell inequalities for relaxed latency constraints

Quantum violations possible with partial communication

Framework applicable to real-world distributed systems

Abstract

Bell inequality violation is the phenomenon where multiple non-communicating parties can exhibit correlations using quantum resources that are impossible if they can only use classical resources. One way to enforce non-communication is to apply a latency constraint: the parties must all produce outputs after they receive their inputs within a time window shorter than the speed of light delay between any pair of parties. If this latency constraint is relaxed so that a subset of the parties can communicate, we can obtain a new set of inequalities on correlations that extends Bell inequalities in a very natural way. Moreover, with this relaxed latency constraint, we can also have quantum communication between a subset of parties and thereby achieve possible quantum violations of these new inequalities. We ultimately wish to answer the fundamental question: "What are the physically realizable correlations between multiple parties under varying latency constraints?" To answer this question, we introduce latency-constrained games, a mathematical framework that extends nonlocal games to the setting where a subset of parties can communicate. The notion of latency-constrained games can have real-world applications, including high frequency trading, distributed computing, computer architecture, and distributed control systems.