A two-qubit Bell inequality for which POVM measurements are relevant

TL;DR

This paper introduces a bipartite Bell inequality that is maximally violated only when POVM measurements are used, highlighting the importance of POVMs in quantum nonlocality tests with two-qubit states.

Contribution

It presents a new Bell inequality that specifically requires POVMs for maximal violation, addressing a question about measurement types in quantum nonlocality.

Findings

Maximal violation occurs only with POVMs, not just projective measurements.

The inequality is maximally violated by maximally entangled two-qubit states.

It answers a question raised by N. Gisin regarding measurement types in Bell tests.

Abstract

A bipartite Bell inequality is derived which is maximally violated on the two-qubit state space if measurements describable by positive operator valued measure (POVM) elements are allowed rather than restricting the possible measurements to projective ones. In particular, the presented Bell inequality requires POVMs in order to be maximally violated by a maximally entangled two-qubit state. This answers a question raised by N. Gisin.