Inequivalence of entanglement, steering, and Bell nonlocality for general measurements

TL;DR

This paper demonstrates that entanglement, steering, and Bell nonlocality are fundamentally different when considering general quantum measurements, extending previous results beyond projective measurements and highlighting the importance of measurement sequences.

Contribution

It proves the inequivalence of entanglement, steering, and nonlocality for general measurements and emphasizes the role of measurement sequences in revealing hidden steering.

Findings

Entanglement, steering, and nonlocality are distinct under general measurements.

Sequences of measurements can reveal hidden steering.

The results extend previous proofs beyond projective measurements.

Abstract

Einstein-Podolsky-Rosen steering is a form of inseparability in quantum theory commonly acknowledged to be intermediate between entanglement and Bell nonlocality. However, this statement has so far only been proven for a restricted class of measurements, namely projective measurements. Here we prove that entanglement, one-way steering, two-way steering and nonlocality are genuinely different considering general measurements, i.e. single round positive-operator-valued-measures. Finally, we show that the use of sequences of measurements is relevant for steering tests, as they can be used to reveal "hidden steering".