Nonlocality Without Entanglement: Quantum Theory and Beyond

TL;DR

This paper explores nonlocality without entanglement (NWE) beyond quantum theory, demonstrating its presence in generalized probabilistic theories and analyzing the structural reasons for its limitations in quantum mechanics.

Contribution

It introduces a framework to compare NWE across theories and reveals that quantum theory's limited NWE stems from its topological state space structure.

Findings

NWE occurs in theories beyond quantum mechanics.

Quantum theory's NWE is limited due to its state space topology.

The framework allows comparison of NWE strength across operational theories.

Abstract

Quantum nonlocality without entanglement (Q-NWE) encapsulates nonlocal behavior of multipartite product states as they may entail global operation for optimal decoding of the classical information encoded within. Here we show that the phenomena of NWE is not specific to quantum theory only, rather a class of generalized probabilistic theories can exhibit such behavior. In fact several manifestations of NWE, e.g., asymmetric local discrimination, suboptimal local discrimination, notion of separable but locally unimplementable measurement arise generically in operational theories other than quantum theory. We propose a framework to compare the strength of NWE in different theories and show that such behavior in quantum theory is limited, suggesting a specific topological feature of quantum theory, namely, the continuity of state space structure. Our work adds profound foundational appeal to the study of NWE phenomena along with its information theoretic relevance.