All pure entangled states can lead to fully nonlocal correlations

TL;DR

This paper demonstrates that all pure entangled states, including non-maximally entangled ones, can exhibit full nonlocality, expanding understanding of quantum correlations beyond maximally entangled states.

Contribution

It establishes a link between full nonlocality and antidistinguishability, showing non-maximally entangled states can be fully nonlocal in any dimension.

Findings

Non-maximally entangled states in d×d spaces (d≥3) can be fully nonlocal.

Simple conditions based on Schmidt coefficients determine full nonlocality.

All pure entangled states can be activated to show full nonlocality in many-copy scenarios.

Abstract

It is a well-established fact that some quantum correlations can be nonlocal, meaning that they cannot be described by a local hidden variable model. Certain quantum correlations have a form of nonlocality so strong that they cannot be reproduced even by models having an arbitrarily small local hidden variable component. These correlations are called fully nonlocal and lead to Bell inequalities in which the maximum quantum value saturates the non-signaling bound. A well-known example of this effect, which is also referred to as quantum pseudo-telepathy or all-versus-nothing proofs of nonlocality, is the quantum distribution fulfilling the Peres-Mermin square, in which the underlying state is a $4\times4$ dimensional maximally entangled state. Other examples of full nonlocality are known but, so far, all of them are for maximally entangled states and it is an open question whether maximal entanglement is necessary for full nonlocality. In this work, we first establish a link between full nonlocality and the concept of antidistinguishability of quantum states. We use this connection to show that in every bipartite $d\times d$ Hilbert space, with $d\geq3$, there are non-maximally entangled states that are fully nonlocal. In fact, we derive simple sufficient conditions for full nonlocality that are only based on the smallest and largest Schmidt coefficients. We also show that in every dimension there exist pure entangled states that do not exhibit full nonlocality. Finally, we show that all pure entangled states can be activated to show full nonlocality in the many-copy scenario.