Complete framework for efficient characterisation of non-Markovian processes

Felix A. Pollock, César Rodríguez-Rosario, Thomas Frauenheim, Mauro Paternostro, Kavan Modi

Research output: Contribution to journalArticlepeer-review


A non-Markovian process is one that retains `memory' of its past. A systematic understanding of these processes is necessary to fully describe and harness a vast range of complex phenomena; however, no such general characterisation currently exists. This long-standing problem has hindered advances in understanding physical, chemical and biological processes, where often dubious theoretical assumptions are made to render a dynamical description tractable. Moreover, the methods currently available to treat non-Markovian quantum dynamics are plagued with unphysical results, like non-positive dynamics. Here we develop an operational framework to characterise arbitrary non-Markovian quantum processes. We demonstrate the universality of our framework and how the characterisation can be rendered efficient, before formulating a necessary and sufficient condition for quantum Markov processes. Finally, we stress how our framework enables the actual systematic analysis of non-Markovian processes, the understanding of their typicality, and the development of new master equations for the effective description of memory-bearing open-system evolution.
Original languageEnglish
JournalPhysical review x
Publication statusSubmitted - 02 Dec 2015


  • quant-ph
  • cond-mat.stat-mech
  • math-ph
  • math.MP


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