title: Nonclassicality of Temporal Correlations.
abstract: The results of spacelike separated measurements are independent of distant measurement settings, a property one might call two-way no-signaling. In contrast, timelike separated measurements are only one-way no-signaling since the past is independent of the future but not vice versa. For this reason some temporal correlations that are formally identical to nonclassical spatial correlations can still be modeled classically. We propose a new formulation of Bell's theorem for temporal correlations; namely, we define nonclassical temporal correlations as the ones which cannot be simulated by propagating in time the classical information content of a quantum system given by the Holevo bound. We first show that temporal correlations between results of any projective quantum measurements on a qubit can be simulated classically. Then we present a sequence of general measurements on a single m-level quantum system that cannot be explained by propagating in time an m-level classical system and using classical computers with unlimited memory.
authors.affiliation: DAMPT, Centre for Mathematical Sciences, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA, United Kingdom.
authors.forename: Stephen
authors.initials: S
authors.lastname: Brierley
authors.affiliation: Inria and Université Paris Diderot, LIAFA, Case 7014, 75205 Paris Cedex 13, France.
authors.forename: Adrian
authors.initials: A
authors.lastname: Kosowski
authors.affiliation: Center for Theoretical Physics, Polish Academy of Sciences, Aleja Lotników 32/46, PL-02-668 Warszawa, Poland.
authors.forename: Marcin
authors.initials: M
authors.lastname: Markiewicz
authors.affiliation: School of Physical and Mathematical Sciences, Nanyang Technological University, 637371 Singapore, Singapore.|Centre for Quantum Technologies, National University of Singapore, 117543 Singapore, Singapore.|MajuLab, CNRS-UNS-NUS-NTU International Joint Research Unit, UMI 3654 Singapore, Singapore.
authors.forename: Tomasz
authors.initials: T
authors.lastname: Paterek
authors.affiliation: Institute of Theoretical Physics and Astrophysics, University of Gdańsk, 80-952 Gdańsk, Poland.|National Quantum Information Centre in Gdańsk, Andersa 27, 81-824 Sopot, Poland.
authors.forename: Anna
authors.initials: A
authors.lastname: Przysiężna