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

Year: 2022

Authors: Gherardini Stefano; Smirne Andrea; Huelga Susana F.; Caruso Filippo

Autors Affiliation: Univ Firenze, Dipartimento Fis & Astron, Via G Sansone 1, I-50019 Sesto Fiorentino, Italy; LENS, CNR, INO, Via N Carrara 1, I-50019 Sesto Fiorentino, Italy; QSTAR, Via N Carrara 1, I-50019 Sesto Fiorentino, Italy; Ist Nazl Fis Nucl, Sez Firenze, Via G Sansone 1, I-50019 Sesto Fiorentino, Italy; Univ Ulm, Inst Theoret Phys, Albert Einstein Allee 11, D-89069 Ulm, Germany; Univ Ulm, IQST, Albert Einstein Allee 11, D-89069 Ulm, Germany; Univ Milan, Dipartimento Fis Aldo Pontremoli, Via Celoria 16, I-20133 Milan, Italy; Ist Nazl Fis Nucl, Sez Milano, Via Celoria 16, I-20133 Milan, Italy.

Abstract: 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.

Journal/Review: QUANTUM SCIENCE AND TECHNOLOGY

Volume: 7 (2)      Pages from: 025005-1  to: 025005-15

More Information: SG and FC were financially supported from PATHOS EU H2020 FET-OPEN Grant No. 828946, the Fondazione CR Firenze through the Project Quantum-AI and UNIFI Grant Q-CODYCES.
KeyWords: quantum non-Markovianity, multi-time statistics, transfer tensor method, transfer-tensor hierarchy, stochastic transfer tensor transformation, non Markovianity in monitored quantum systems
DOI: 10.1088/2058-9565/ac4422

Citations: 7
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