title: Quantifying Non-Markovianity with Temporal Steering.
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.
authors.affiliation: Department of Physics and National Center for Theoretical Sciences, National Cheng-Kung University, Tainan 701, Taiwan.
authors.forename: Shin-Liang
authors.initials: SL
authors.lastname: Chen
authors.affiliation: CEMS, RIKEN, 351-0198 Wako-shi, Japan.
authors.forename: Neill
authors.initials: N
authors.lastname: Lambert
authors.affiliation: Department of Engineering Science, National Cheng-Kung University, Tainan City 701, Taiwan.
authors.forename: Che-Ming
authors.initials: CM
authors.lastname: Li
authors.affiliation: CEMS, RIKEN, 351-0198 Wako-shi, Japan.|Faculty of Physics, Adam Mickiewicz University, 61-614 Poznań, Poland.
authors.forename: Adam
authors.initials: A
authors.lastname: Miranowicz
authors.affiliation: Department of Physics and National Center for Theoretical Sciences, National Cheng-Kung University, Tainan 701, Taiwan.|CEMS, RIKEN, 351-0198 Wako-shi, Japan.
authors.forename: Yueh-Nan
authors.initials: YN
authors.lastname: Chen
authors.affiliation: CEMS, RIKEN, 351-0198 Wako-shi, Japan.|Department of Physics, The University of Michigan, Ann Arbor, Michigan 48109-1040, USA.
authors.forename: Franco
authors.initials: F
authors.lastname: Nori