A formalism for steering with local quantum measurements

TL;DR

This paper introduces a comprehensive framework for classical, quantum, and post-quantum steering using uncharacterised measurements, connecting to entanglement witnesses and defining a new quantifier called negativity of post-quantum steering.

Contribution

It develops a unified formalism for steering, introduces new assemblage families via positive maps and unextendible bases, and proposes a quantifier for post-quantum steering.

Findings

Post-quantum assemblages can be constructed with quantum correlations in Bell tests.

The negativity of post-quantum steering is a convex monotone.

The framework links steering to entanglement witnesses and unifies classical, quantum, and post-quantum cases.

Abstract

We develop a unified approach to classical, quantum and post-quantum steering. The framework is based on uncharacterised (black-box) parties performing quantum measurements on their share of a (possibly unphysical) quantum state, and its starting point is the characterisation of general no-signalling assemblages via non-positive local hidden-state models. By developing a connection to entanglement witnesses, this formalism allows for new definitions of families of assemblages, in particular via (i) non-decomposable positive maps and (ii) unextendible product bases. The former proves to be useful for constructing post-quantum assemblages with the built-in feature of yielding only quantum correlations in Bell experiments, while the latter always gives certifiably post-quantum assemblages. Finally, our framework is equipped with an inherent quantifier of post-quantum steering, which we call the negativity of post-quantum steering. We postulate that post-quantum steering should not increase under one-way quantum operations from the steered parties to the steering parties, and we show that, in this sense, the negativity of post-quantum steering is a convex post-quantum-steering monotone.