Bounds on quantum nonlocality via partial transposition

TL;DR

This paper establishes bounds linking quantum nonlocality violations to state distinguishability, providing insights into the limitations of certain quantum states in device-independent quantum information tasks.

Contribution

It introduces bounds connecting Bell inequality violations with state discrimination measures and extends these bounds to asymptotic scenarios involving partial transposition.

Findings

Bell violation bounds are related to state distinguishability.

For PPT states, the asymptotic nonlocality is bounded by the relative entropy of entanglement.

Limits are identified for the use of private key states in device-independent scenarios.

Abstract

We explore the link between two concepts: the level of violation of a Bell inequality by a quantum state and discrimination between two states by means of restricted classes of operations, such as local operations and classical communication (LOCC) and separable ones. For any bipartite Bell inequality, we show that its value on a given quantum state cannot exceed the classical bound by more than the maximal quantum violation shrunk by a factor related to distinguishability of this state from the separable set by means of some restricted class of operations. We then consider the general scenarios where the parties are allowed to perform a local pre-processing of many copies of the state before the Bell test (asymptotic and hidden-nonlocality scenarios). We define the asymptotic relative entropy of nonlocality and, for PPT states, we bound this quantity by the relative entropy of entanglement of the partially transposed state. The bounds are strong enough to limit the use of certain states containing private key in the device-independent scenario.