Unification of witnessing initial system-environment correlations and witnessing non-Markovianity

¹ Bremen Center for Computational Materials Science, Universität Bremen - Am Fallturm 1, 28359 Bremen, Germany, EU
² Department of Physics, University of Oxford, Clarendon Laboratory - Oxford, UK, EU
³ Centre for Quantum Technologies, National University of Singapore - Singapore
⁴ Centre for Theoretical Atomic, Molecular and Optical Physics, School of Mathematics and Physics, Queen's University Belfast - BT7 1NN Belfast, UK, EU
⁵ Department of Chemistry and Chemical Biology, Harvard University - Cambridge, MA, USA

^(a) cesar.rodriguez@bccms.uni-bremen.de

Received: 30 April 2012
Accepted: 26 June 2012

Abstract

We show the connection between a witness that detects dynamical maps with initial system-environment correlations and a witness that detects non-Markovian open quantum systems. Our analysis is based on studying the role that state preparation plays in witnessing violations of contractivity of open-quantum-system dynamics. Contractivity is a property of some quantum processes where the trace distance of density matrices decrease with time. From this, we show how a witness of initial correlations is an upper bound to a witness of non-Markovianity. We discuss how this relationship shows further connections between initial system-environment correlations and non-Markovianity, at an instance of time, in open quantum systems.