Certifying the purity of quantum states with temporal correlations

TL;DR

This paper demonstrates how temporal correlations from measurement sequences can be used to certify the purity of quantum states in a semi-device independent manner, providing insights into state preparation and entanglement.

Contribution

It introduces a method to bound the purity of quantum states using temporal correlations, extending semi-device independent certification techniques.

Findings

Bounds on initial state purity established from temporal correlations.

Method to infer upper bounds on concurrence in joint systems.

Application to assess state preparation quality and measurement implementation.

Abstract

Correlations obtained from sequences of measurements have been employed to distinguish among different physical theories or to witness the dimension of a system. In this work we show that they can also be used to establish semi-device independent lower bounds on the purity of the initial quantum state or even on one of the post-measurement states. For single systems this provides information on the quality of the preparation procedures of pure states or the implementation of measurements with anticipated pure post-measurement states. For joint systems one can combine our bound with results from entanglement theory to infer an upper bound on the concurrence based on the temporal correlations observed on a subsystem.