Strengthened Bell Inequalities for Entanglement Verification

TL;DR

This paper develops strengthened Bell inequalities that, under certain assumptions, can more reliably verify entanglement by relating Bell violations to the negativity measure, and shows that entanglement is more common than Bell violation in two-qubit states.

Contribution

It introduces generalized strengthened Bell inequalities linked to negativity, enhancing entanglement verification methods.

Findings

Violating strengthened Bell inequalities is rarer than being entangled.

The expectation value of the Bell operator relates to negativity.

Strengthened inequalities improve entanglement verification reliability.

Abstract

Bell inequalities were meant to test quantum mechanics vs local hidden variable models, but can also be used to verify entanglement. For entanglement verification purposes one assumes the validity of quantum mechanics as well as quantum descriptions of one's measurements. With the help of these assumptions it is possible to derive a strengthened Bell inequality whose violation implies entanglement. We generalize known examples of such inequalities by relating the expectation value of the Bell operator to a particular quantitative measure of entanglement, namely the negativity. Moreover, we obtain statistics illustrating the fact that violating a given (strengthened or not) Bell inequality is a much more rare feat for a quantum state of two qubits than it is to be entangled.