Resource Theories of Multi-Time Processes: a Window Into Quantum Non-Markovianity
Resource theories of multi-time processes: A window into quantum non-Markovianity Graeme D. Berk1, Andrew J. P. Garner2,3, Benjamin Yadin4, Kavan Modi1, and Felix A. Pollock1 1School of Physics and Astronomy, Monash University, Clayton, Victoria 3800, Australia 2Institute for Quantum Optics and Quantum Information, Austrian Academy of Sciences, Boltzmanngasse 3, A-1090 Vienna, Austria 3School of Physical and Mathematical Sciences, Nanyang Technological University, 21 Nanyang Link, 637371, Singapore 4School of Mathematical Sciences, University of Nottingham, University Park, Nottingham NG7 2RD, United Kingdom. April 8, 2021 We investigate the conditions under which an uncontrolled background process may be harnessed by an agent to perform a task that would otherwise be impossible within their operational framework. This situation can be understood from the perspective of resource theory: rather than harnessing ‘useful’ quantum states to perform tasks, we propose a resource theory of quantum processes across multiple points in time. Uncontrolled background processes fulfil the role of resources, and a new set of objects called superprocesses, corresponding to operationally implementable control of the system undergoing the process, constitute the transformations between them. After formally introducing a framework for deriving resource theories of multi-time processes, we present a hierarchy of examples induced by restricting quantum or classical communication within the superprocess – corresponding to a client-server scenario. The resulting nine resource theories have different notions of quantum or classical memory as the determinant of their utility. Furthermore, one of these theories has a strict correspondence between non- useful processes and those that are Markovian and, therefore, could be said to be a true ‘quantum resource theory of non-Markovianity’.
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