A formalism for steering with local quantum measurements

Sainz, A B and Aolita, L and Piani, M and Hoban, M J and Skrzypczyk, P (2018) A formalism for steering with local quantum measurements. New Journal of Physics, 20. ISSN 1367-2630

[img]
Preview
Text (Sainz-etal-NJP-2018-A-formalism-for-steering-with-local-quantum-measurements)
Sainz_etal_NJP_2018_A_formalism_for_steering_with_local_quantum_measurements.pdf
Final Published Version
License: Creative Commons Attribution 3.0 logo

Download (530kB)| Preview

    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.