Exact nonequilibrium quantum observable statistics: A large-deviation approach

Gherardini, Stefano

doi:10.1103/physreva.99.062105

“…Being the single quantum measurement a dynamical process with probabilistic nature, it is customary to associate to any sequence of them a stochastic process obeying, over time, to a specific probability distribution [2,5]. Such distribution usually depends on properties relying on both the system and the measured observable, and even external sources of noise [6,7].…”

Section: Introductionmentioning

confidence: 99%

“…(20) and the corresponding histogram (blue areas). The latter has been obtained by numerically repeating the non-equilibrium dynamics of sequential measurements over 10 6 realizations on a spin s =7 2 . In the three panels, the initial state ρ 0 has been thermal with inverse temperature, respectively equal to β = 0, β = 0.5 and β = 1.…”

mentioning

confidence: 99%

Thermalization processes induced by quantum monitoring in multi-level systems

Gherardini,

Giachetti,

Ruffo

et al. 2020

Preprint

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We study the heat statistics of an N -dimensional quantum system monitored by a sequence of projective measurements. The late-time, asymptotic properties of the heat characteristic function are analyzed in the thermodynamic limit of a high, ideally infinite, number of measurements. In this context, conditions allowing for Infinite-Temperature Thermalization (ITT), induced by the monitoring of the quantum system, are discussed. We show that ITT is identified by the fixed point of a symmetric random matrix that models the stochastic process originated by the sequence of measurements. Such fixed point is independent on the non-equilibrium evolution of the system and its initial state. Exceptions to ITT take place when the observable of the intermediate measurements is commuting (or quasi-commuting) with the Hamiltonian of the system, or when the time interval between measurements is smaller or comparable with the energy scale of the quantum system (quantum Zeno regime). Results on the limit of infinite-dimensional Hilbert spaces (N → ∞) -describing continuous systems with a discrete spectrum -are presented. By denoting with M the number of quantum measurements, we show that the order of the limits M → ∞ and N → ∞ matters: when N is fixed and M diverges, then there is ITT. In the opposite case, the system becomes classical, so that the measurements are no longer effective in changing the state of the system. A non trivial result is obtained fixing M/N 2 where partial ITT occurs. Finally, an example of incomplete thermalization applicable to rotating two-dimensional gases is presented.

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“…Hopefully, our results will provide useful insights to look for such rigorous connections. More in general, our analysis suggests the usefulness of the TT approach also to deal with multi-time statistics; a further example in this direction might be to use the hierarchy of stochastic TTs to evaluate the non-Markovianity along the so-called most probable trajectory of the system, namely the trajectory originated with higher probability by a sequence of quantum measurements [47,48].…”

Section: Discussionmentioning

confidence: 93%

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

Gherardini,

Smirne,

Huelga

et al. 2021

Preprint

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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, which provides us with relevant information about the role of correlations between the system and the environment in the dynamics. The connection between the transfer-tensor 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 1-step transfer tensors only. On the other hand, we introduce the set of stochastic transfer tensor transformations associated with local measurements on the open system at different times and conditioned on the measurement outcomes. The use of the transfer-tensor 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 spinboson case study.

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“…Hopefully, our results will provide useful insights to look for such rigorous connections. More in general, our analysis suggests the usefulness of the TT approach also to deal with multi-time statistics; an example in this direction might be to use the hierarchy of stochastic TTs to evaluate the non-Markovianity along the so-called most probable trajectory of the system, namely the trajectory originated with higher probability by a sequence of quantum measurements [52,53]. In addition, the TT formalism addressed in this paper is also expected to provide a powerful tool to evaluate experimentally the degree of non-Markovianity [54] in monitored quantum dynamics [55,56], as well as to test the validity of the quantum regression theorem or possible generalizations [11,57,58].…”

Section: Discussionmentioning

confidence: 99%

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

Gherardini¹,

Smirne²,

Huelga³

et al. 2022

Quantum Sci. Technol.

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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, which provides us with relevant information about the role of correlations between the system and the environment in the dynamics. The connection between the transfer-tensor 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 1-step transfer tensors only. On the other hand, we introduce the set of stochastic transfer tensor transformations associated with local measurements on the open system at different times and conditioned on the measurement outcomes. The use of the transfer-tensor 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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Exact nonequilibrium quantum observable statistics: A large-deviation approach

Cited by 8 publications

References 42 publications

Thermalization processes induced by quantum monitoring in multi-level systems

Thermalization processes induced by quantum monitoring in multi-level systems

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

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

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