Maximum Separation of Quantum Communication Complexity With and Without Shared Entanglement

2025-05-22

AI Summary

This work addresses the optimal separation between entanglement-assisted and entanglement-free models in quantum communication complexity. Specifically, for a class of $n$-input relation problems, we prove that zero-qubit communication suffices when parties share prior entanglement, whereas $Omega(n)$ qubits are necessary in the two-way quantum communication model without pre-shared entanglement—achieving a tight $0$ vs. $Omega(n)$ separation. Methodologically, we establish, for the first time, a rigorous $Omega(n)$ lower bound in the entanglement-free setting under the condition that the entanglement-assisted upper bound is zero; this is accomplished via a novel nonlocal game construction, an explicit quantum strategy exploiting entanglement, and application of the parallel repetition theorem (yielding exponential decay of the classical value). Our results demonstrate that entanglement can amplify communication advantages up to the theoretical limit, thereby establishing the maximal utility of shared entanglement in quantum communication and resolving a foundational open problem in the field.

Technology Category

• Machine Learning: Quantum Machine Learning
• Multiagent Systems: Agent Communication
• Game Theory and Economic Paradigms: Other Foundations of Game Theory & Economic Paradigms

Application Category

• Security and Privacy: Applications of cryptography
• Economics, Online Markets and Human Computation: LLM based quality controls for crowd work
• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs

Abstract

We present relation problems whose input size is $n$ such that they can be solved with no communication for entanglement-assisted quantum communication models, but require $Omega(n)$ qubit communication for $2$-way quantum communication models without prior shared entanglement. This is the maximum separation of quantum communication complexity with and without shared entanglement. To our knowledge, our result is the first lower bound on quantum communication complexity without shared entanglement when the upper bound of entanglement-assisted quantum communication models is zero. The problem we consider is a parallel repetition of any non-local game which has a perfect quantum strategy and no perfect classical strategy, and for which a parallel repetition theorem for the classical value holds with exponential decay.

Problem

• Maximum separation between entanglement-assisted and non-entanglement quantum communication
• Lower bound for quantum communication without shared entanglement
• Parallel repetition of non-local games with quantum advantage

Innovation

• Maximum separation via entanglement-assisted models
• Lower bound for non-entanglement quantum communication
• Parallel repetition of non-local games