Locally inaccessible hidden quantum correlations

TL;DR

This paper demonstrates the theoretical existence of hidden quantum correlations in two-qubit states that cannot be revealed by local filters on one side but can be uncovered through cooperation, under a conjecture about quantum steering ellipsoids.

Contribution

It introduces a necessary criterion for identifying locally inaccessible hidden quantum correlations in two-qubit states, based on a conjecture about quantum steering ellipsoids.

Findings

Existence of two-qubit states with hidden quantum correlations inaccessible locally

Explicit examples of states with maximal hidden quantum correlations

Support for the conjecture through numerical evidence

Abstract

We prove, modulo a conjecture on quantum steering ellipsoids being true, the existence of the phenomenon of locally inaccessible hidden quantum correlations. That is, the existence of two-particle states whose hidden quantum correlations cannot be revealed by local filters implemented exclusively on one side of the experiment, but that can still be revealed when both parties cooperate in applying judiciously chosen local filters. The quantum correlations here considered are the violation of the CHSH-inequality for Bell-nonlocality and the violation of the $\rm F_3$-inequality for EPR-steering. Specifically, we provide a necessary criterion for guaranteeing the presence of such phenomenon for arbitrary two-qubit states. This criterion in turn relies on the conjecture that the maximal violation of CHSH-inequality and $\rm F_3$-inequality are both upper bounded by functions that depend on the magnitude of the quantum steering ellipsoid centre. This latter conjecture, although currently lacking an analytical proof, is supported by numerical results. We use this necessary criterion to explicitly show examples of two-qubit states with locally inaccessible hidden quantum correlations and, furthermore, two-qubit states with locally inaccessible maximal hidden quantum correlations.