Investigating the generality of time-local master equations

Maldonado-Mundo, Daniel; Öhberg, Patrik; Lovett, Brendon W.; Andersson, Erika

doi:10.1103/physreva.86.042107

Cited by 24 publications

(18 citation statements)

References 21 publications

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“…Since the commutation relations (8) imply that there exists an environmental basis {|n(t) } which diagonalizeŝ R 00 (t),ŵ 0 (t)ŵ † 1 (t), andŵ 1 (t)ŵ † 0 (t) at time t, we can write all three operators with the help of this basis,…”

Section: Separability For a Qubitmentioning

confidence: 99%

“…In general the quantification of entanglement requires the knowledge of the whole system-environment density matrix. For open quantum systems with large environments, this is easier to have in theory than in experiment, but is often also challenging theoretically, since many of the standard approximate methods are inapplicable in this case [6][7][8][9], since their aim is to provide the evolution of the system of interest alone. Only then can the numerical calculation of an entanglement measure be performed (one that can be found from a density matrix for larger systems, such as Negativity [10][11][12]).…”

Section: Introductionmentioning

confidence: 99%

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Criteria for system-environment entanglement generation for systems of any size in pure-dephasing evolutions

Roszak

2018

Phys. Rev. A

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An evolution between a system and its environment which leads to pure dephasing of the system may either be a result of entanglement building up between the system and the environment or not (the second option is only possible for initially mixed environmental states). We find a way of distinguishing between an entangling and non-entangling evolutions for systems which are larger than a single qubit. The generalization of the single qubit separability criterion to larger systems is not sufficient to make this distinction (it constitutes a necessary condition of separability). A set of additional conditions for the operators describing the evolution of the environment depending on the state of the system is required. We find that the commutation of these environmental operators with the initial state of the environment does not guarantee separability, products of the operators need to commute among themselves for a pure dephasing evolution not to be accompanied by system-environment entanglement generation. This is a qualitative difference with respect to the single-qubit case, since it allows for a system to entangle with an initially completely mixed environment.PACS numbers:

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Section: Separability For a Qubitmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Criteria for system-environment entanglement generation for systems of any size in pure-dephasing evolutions

Roszak

2018

Phys. Rev. A

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“…Nevertheless, many open systems can be described by a time-local ME and this assumptions seems to be less strict than one might initially guess. See Refs [35,36]. for further research on this topic.…”

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confidence: 99%

Non-Markovianity and negative entropy production rates

2019

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Entropy production plays a fundamental role in nonequilibrium thermodynamics to quantify the irreversibility of open systems. Its positivity can be ensured for a wide class of setups, but the entropy production rate can become negative sometimes. This is often taken as an indicator of non-Markovianity. We make this link precise by showing under which conditions a negative entropy production rate implies non-Markovianity and when it does not. For a system coupled to a single heat bath this can be established within a unified language for two setups: (i) the dynamics resulting from a coarse-grained description of a Markovian master equation and (ii) the classical Hamiltonian dynamics of a system coupled to a bath. The quantum version of the latter result is shown not to hold despite the fact that the integrated thermodynamic description is formally equivalent to the classical case. The instantaneous fixed point of a non-Markovian dynamics plays an important role in our study. Our key contribution is to provide a consistent theoretical framework to study the finite-time thermodynamics of a large class of dynamics with a precise link to its non-Markovianity. arXiv:1806.09101v3 [cond-mat.stat-mech]

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“…in [16,18,23], but the significance and usefulness of the unique diagonal form of the equation has, as far as we are aware, not been emphasized. Neither is the generality of time-local master equations [24] as widely recognised as it should be. We will therefore start by presenting the canonical form of a time-local master equation in Sec.…”

Section: Introductionmentioning

confidence: 99%

Canonical form of master equations and characterization of non-Markovianity

et al. 2014

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Master equations govern the time evolution of a quantum system interacting with an environment, and may be written in a variety of forms. Time-independent or memoryless master equations, in particular, can be cast in the well-known Lindblad form. Any time-local master equation, Markovian or non-Markovian, may in fact also be written in a Lindblad-like form. A diagonalisation procedure results in a unique, and in this sense canonical, representation of the equation, which may be used to fully characterize the non-Markovianity of the time evolution. Recently, several different measures of non-Markovianity have been presented which reflect, to varying degrees, the appearance of negative decoherence rates in the Lindblad-like form of the master equation. We therefore propose using the negative decoherence rates themselves, as they appear in the canonical form of the master equation, to completely characterize non-Markovianity. The advantages of this are especially apparent when more than one decoherence channel is present. We show that a measure proposed by Rivas et al. is a surprisingly simple function of the canonical decoherence rates, and give an example of a master equation that is non-Markovian for all times t > 0, but to which nearly all proposed measures are blind. We also give necessary and sufficient conditions for trace distance and volume measures to witness non-Markovianity, in terms of the Bloch damping matrix.

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Investigating the generality of time-local master equations

Cited by 24 publications

References 21 publications

Criteria for system-environment entanglement generation for systems of any size in pure-dephasing evolutions

Criteria for system-environment entanglement generation for systems of any size in pure-dephasing evolutions

Non-Markovianity and negative entropy production rates

Canonical form of master equations and characterization of non-Markovianity

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