Dynamical maps beyond Markovian regime

Chruściński, Dariusz

doi:10.1016/j.physrep.2022.09.003

Cited by 43 publications

(25 citation statements)

References 304 publications

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“…[70,71] (and thus map a quantum state to another proper quantum state). The contrapositive of Lindblad's theorem thus imposes that our master equation is non-Markovian [32,41,[72][73][74][75][76][77][78].…”

Section: Interpretating the Master Equationmentioning

confidence: 99%

Benchmarking the cosmological master equations

2022

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Master equations are commonly employed in cosmology to model the effect of additional degrees of freedom, treated as an “environment”, onto a given “system”. However, they rely on assumptions that are not necessarily satisfied in cosmology, where the environment may be out of equilibrium and the background is dynamical. In this work, we apply the master-equation program to a model that is exactly solvable, and which consists of two linearly coupled scalar fields evolving on a cosmological background. The light field plays the role of the system and the heavy field is the environment. By comparing the exact solution to the output of the master equation, we can critically assess its performance. We find that the master equation exhibits a set of “spurious” terms that explicitly depend on the initial conditions, and which arise as a consequence of working on a dynamical background. Although they cancel out in the perturbative limit of the theory (i.e. at leading orders in the interaction strength), they spoil resummation. However, when those terms are removed, the master equation performs impressively well to reproduce the power spectra and the amount of the decoherence of the light field, even in the strongly decohered regime. We conclude that master equations are able to perform late-time resummation, even though the system is far from the Markovian limit, provided spurious contributions are suppressed.

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Section: Interpretating the Master Equationmentioning

confidence: 99%

Benchmarking the cosmological master equations

2022

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“…One should always take into account this ambiguity when dealing with concepts of (non–)Markovianity in open quantum systems (cf. the recent reviews 9 – 12 ). The approach of 3 , 4 adopted in this paper is closely related to the mathematical formulation of quantum Markov stochastic processes proposed in 13 – 15 (cf.…”

Section: Introductionmentioning

confidence: 99%

On Markovianity and classicality in multilevel spin–boson models

Chruściński

Hesabi

Lonigro

2023

Sci Rep

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We provide a detailed discussion about the unitary and reduced evolution induced by family of Hamiltonian models describing a multilevel system, with a ground state and a possibly multilevel excited sector, coupled to a multimode boson field via a rotating-wave interaction. We prove explicitly that the system, in the limit in which the coupling is flat with respect to the boson frequencies, is Markovian under sharp measurements in arbitrary bases; we also find necessary and sufficient conditions under which the process is classical, i.e. its family of multitime joint probability distributions satisfies the Kolmogorov consistency condition, and may thus be equivalently obtained by a classical stochastic process.

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“…A particular class of non-Markovian ME, the generalized Markovian master equation (GMME) is often exactly solvable via Laplace transforms [21][22][23][24]. This ME describes a system undergoing Markovian dephasing while coupled to a non-Markovian environment with some finite memory.…”

Section: Introductionmentioning

confidence: 99%

Master equation emulation and coherence preservation with classical control of a superconducting qubit

Vlachos

Zhang²,

Maurya³

et al. 2022

Phys. Rev. A

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Open quantum systems are a topic of intense theoretical research. The use of master equations to model a system's evolution subject to an interaction with an external environment is one of the most successful theoretical paradigms. General experimental tools to study different open system realizations have been limited, and so it is highly desirable to develop experimental tools which emulate diverse master equation dynamics and give a way to test open systems theories. In this paper we demonstrate a systematic method for engineering specific system-environment interactions and emulating master equations of a particular form using classical stochastic noise. We also demonstrate that non-Markovian noise can be used as a resource to extend the coherence of a quantum system and counteract the adversarial effects of Markovian environments.

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Dynamical maps beyond Markovian regime

Cited by 43 publications

References 304 publications

Benchmarking the cosmological master equations

Benchmarking the cosmological master equations

On Markovianity and classicality in multilevel spin–boson models

Master equation emulation and coherence preservation with classical control of a superconducting qubit

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