Quantifying Non-Markovianity with Temporal Steering

Shin-Liang Chen, Neill Lambert, Che-Ming Li, Adam Miranowicz, Yueh-Nan Chen, and Franco Nori

Phys. Rev. Lett. 116, 020503 – Published 15 January 2016

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 programing, 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 nonincreasing function under completely positive trace-preserving maps and can be used to define a sufficient and practical measure of strong non-Markovianity.

Received 7 August 2015

DOI:https://doi.org/10.1103/PhysRevLett.116.020503

Physics Subject Headings (PhySH)

Entanglement measures Open quantum systems Quantum entanglement

Atomic, Molecular & OpticalGeneral Physics

Authors & Affiliations

Shin-Liang Chen¹, Neill Lambert², Che-Ming Li³, Adam Miranowicz^2,4, Yueh-Nan Chen^1,2,*, and Franco Nori^2,5

¹Department of Physics and National Center for Theoretical Sciences, National Cheng-Kung University, Tainan 701, Taiwan
²CEMS, RIKEN, 351-0198 Wako-shi, Japan
³Department of Engineering Science, National Cheng-Kung University, Tainan City 701, Taiwan
⁴Faculty of Physics, Adam Mickiewicz University, 61-614 Poznań, Poland
⁵Department of Physics, The University of Michigan, Ann Arbor, Michigan 48109-1040, USA