Quantifying Non-Markovianity with Temporal Steering

TL;DR

This paper introduces a method to quantify temporal quantum steering, enabling the measurement of non-Markovianity in quantum systems through semidefinite programming, advancing understanding of quantum correlations over time.

Contribution

It develops a semidefinite programming-based measure called temporal steerable weight, providing a practical way to quantify non-Markovianity in quantum processes.

Findings

Temporal steerable weight is non-increasing under CPTP maps.

The measure effectively quantifies strong non-Markovianity.

The approach parallels EPR steerable weight, adapted for temporal correlations.

Abstract

Einstein-Podolsky-Rosen (EPR) steering is a type of quantum correlation which allows one to remotely prepare, or steer, the state of a distant quantum system. While EPR steering can be thought of as a purely spatial correlation there does exist a temporal analogue, in the form of single-system temporal steering. However, a precise quantification of such temporal steering has been lacking. Here we show that it can be measured, via semidefinite programming, with a temporal steerable weight, in direct analogy to the recently proposed EPR steerable weight. We find a useful property of the temporal steerable weight in that it is a non-increasing function under completely-positive trace-preserving maps and can be used to define a sufficient and practical measure of strong non-Markovianity.