4.6 Article

Transfer-tensor description of memory effects in open-system dynamics and multi-time statistics

Journal

QUANTUM SCIENCE AND TECHNOLOGY
Volume 7, Issue 2, Pages -

Publisher

IOP Publishing Ltd
DOI: 10.1088/2058-9565/ac4422

Keywords

quantum non-Markovianity; multi-time statistics; transfer tensor method; transfer-tensor hierarchy; stochastic transfer tensor transformation; non Markovianity in monitored quantum systems

Funding

  1. PATHOS EU H2020 FET-OPEN [828946]
  2. Fondazione CR Firenze through the Project Quantum-AI
  3. UNIFI Grant Q-CODYCES

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The non-Markovianity of an arbitrary open quantum system is analyzed by studying its multi-time statistics given by monitoring at discrete times. The hierarchy of inhomogeneous transfer tensors (TTs) is exploited to understand the role of correlations between the system and the environment in the dynamics. Stochastic TT transformations associated with local measurements at different times are introduced, allowing for comparison of memory effects in the multi-time statistics with those in non-monitored non-Markovian dynamics.
The non-Markovianity of an arbitrary open quantum system is analyzed in reference to the multi-time statistics given by its monitoring at discrete times. On the one hand, we exploit the hierarchy of inhomogeneous transfer tensors (TTs), which provides us with relevant information about the role of correlations between the system and the environment in the dynamics. The connection between the TT hierarchy and the CP-divisibility property is then investigated, by showing to what extent quantum Markovianity can be linked to a description of the open-system dynamics by means of the composition of one-step TTs only. On the other hand, we introduce the set of stochastic TT transformations associated with local measurements on the open system at different times and conditioned on the measurement outcomes. The use of the TT formalism accounts for different kinds of memory effects in the multi-time statistics and allows us to compare them on a similar footing with the memory effects present in non-monitored non-Markovian dynamics, as we illustrate on a spin-boson case study.

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