Certifying Temporal Correlations

TL;DR

This paper extends self-testing to sequential quantum measurements, demonstrating unique SDP optimizers, robustness to deviations, and using maximal violations to certify quantum channels, thus broadening quantum device certification methods.

Contribution

It introduces a novel framework for certifying quantum channels via sequential measurement inequalities, with unique SDP solutions and robustness analysis, bridging spatial and temporal quantum correlations.

Findings

Unique optimizer matrices in SDP for sequential measurements.

Robustness of optimal solutions to small deviations.

Maximal violations certify quantum channels up to isometries.

Abstract

Self-testing has been established as a major approach for quantum device certification based on experimental statistics under minimal assumptions. However, despite more than 20 years of research effort most of the self-testing protocols are restricted to spatial scenarios (Bell scenarios), without any temporal generalisations known. Under the scenario of sequential measurements performed on a single quantum system, we build upon previous works which used semi-definite programming (SDP) based methods to bound sequential measurement inequalities. For such SDPs, we show that the optimiser matrix is unique and moreover this uniqueness is robust to small deviations from the quantum bound. Further, we consider a generalised scenario in presence of quantum channels and draw analogies in the structure of Bell and sequential inequalities using the pseudo-density matrix formalism. These analogies allow us to show a practical use of maximal violations of sequential inequalities in the form of certification of quantum channels up to isometries.