Semi-device-independently characterizing quantum temporal correlations

TL;DR

This paper introduces a versatile, device-independent framework for characterizing quantum temporal correlations, applicable in scenarios with uncharacterized or partially characterized quantum devices, and explores various quantum certification applications.

Contribution

It develops a general framework for quantum temporal correlations that is device-independent and adaptable to semi-device-independent constraints, enabling new quantum certification methods.

Findings

Proves quantum separations over local hidden variable models under certain constraints

Provides bounds on temporal Bell inequality violations

Quantifies temporal steerability and randomness access code success probabilities

Abstract

We develop a framework for characterizing quantum temporal correlations in a general temporal scenario, in which an initial quantum state is measured, sent through a quantum channel, and finally measured again. This framework does not make any assumptions on the system nor on the measurements, namely, it is device-independent. It is versatile enough, however, to allow for the addition of further constraints in a semi-device-independent setting. Our framework serves as a natural tool for quantum certification in a temporal scenario when the quantum devices involved are uncharacterized or partially characterized. It can hence also be used for characterizing quantum temporal correlations when one assumes an additional constraint of no-signalling in time, there are upper bounds on the involved systems' dimensions, rank constraints -- for which we prove genuine quantum separations over local hidden variable models -- or further linear constraints. We present a number of applications, including bounding the maximal violation of temporal Bell inequalities, quantifying temporal steerability, bounding the maximum successful probability in quantum randomness access codes.