Certifying nonlocal properties of noisy quantum operations

TL;DR

This paper develops a unified method to certify nonlocal properties of noisy quantum channels using prepare-and-measure protocols, analyzing how different noise models affect the certification process and identifying cases where noise can induce nonlocality.

Contribution

It extends existing certification methods to quantum channels under noise, providing new criteria and simple tests for certifying nonlocality in noisy environments.

Findings

Certain noise models can generate nonlocality and entanglement.

Complete dephasing simplifies nonlocality certification protocols.

Relations between bipartite channels and classical stochastic matrices are key to the tests.

Abstract

Certifying quantum properties from the probability distributions they induce is an important task for several purposes. While this framework has been largely explored and used for quantum states, its extrapolation to the level of channels started recently in a variety of approaches. In particular, little is known about to what extent noise can spoil certification methods for channels. In this work we provide a unified methodology to certify nonlocal properties of quantum channels from the correlations obtained in prepare-and-measurement protocols: our approach gathers fully and semi-device-independent existing methods for this purpose, and extends them to new certification criteria. In addition, the effect of different models of dephasing noise is analysed. Some noise models are shown to generate nonlocality and entanglement in special cases. In the extreme case of complete dephasing, the measurement protocols discussed yield particularly simple tests to certify nonlocality, which can be obtained from known criteria by fixing the dephasing basis. These are based on the relations between bipartite quantum channels and their classical analogues: bipartite stochastic matrices defining conditional distributions.