Admissible memory kernels for random unitary qubit evolution

Wudarski, Filip; Należyty, Paweł; Sarbicki, Gniewomir; Chruściński, Dariusz

doi:10.1103/physreva.91.042105

Cited by 36 publications

(32 citation statements)

References 48 publications

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“…However, mixing of quantum dynamical maps leads to new time evolutions, whose Markovianity properties can be related in a quite counter-intuitive way to the Markovianity of the original maps [18][19][20][21][22][23]. In particular one can consider random mixtures of unitary evolutions showing up memory effects, so that objections have been raised about the validity of the interpretation of non-Markovianity in terms of information flow [24,25].…”

Section: Introductionmentioning

confidence: 99%

Mixing-induced quantum non-Markovianity and information flow

2018

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Keywords: open quantum systems, non-Markovian quantum dynamics, distinguishability of quantum states, mixing quantum dynamical maps, system-environment correlations, information flow Abstract Mixing dynamical maps describing open quantum systems can lead from Markovian to non-Markovian processes. Being surprising and counter-intuitive, this result has been used as argument against characterization of non-Markovianity in terms of information exchange. Here, we demonstrate that, quite the contrary, mixing can be understood in a natural way which is fully consistent with existing theories of memory effects. In particular, we show how mixing-induced non-Markovianity can be interpreted in terms of the distinguishability of quantum states, systemenvironment correlations and the information flow between system and environment.

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Section: Introductionmentioning

confidence: 99%

Mixing-induced quantum non-Markovianity and information flow

2018

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“…We recall that such a map is a complete positive trace preserving one of the class of random unitaries [2,37]. A nice feature of this dynamical map is that, if the initial state of the the open system AB at t = 0 belongs to the class of Bell-diagonal states, the evolved state will remain within such a class for each t > 0.…”

Section: The Systemmentioning

confidence: 99%

Distributed correlations and information flows within a hybrid multipartite quantum-classical system

Leggio¹,

Franco²,

Soares-Pinto³

et al. 2015

Phys. Rev. A

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Understanding the non-Markovian mechanisms underlying the revivals of quantum entanglement in the presence of classical environments is central in the theory of quantum information. Tentative interpretations have been given by either the role of the environment as a control device or the concept of hidden entanglement. We address this issue from an information-theoretic point of view. To this aim, we consider a paradigmatic tripartite system, already realized in the laboratory, made of two independent qubits and a random classical field locally interacting with one qubit alone. We study the dynamical relationship between the two-qubit entanglement and the genuine tripartite correlations of the overall system, finding that collapse and revivals of entanglement correspond, respectively, to the rise and fall of the overall tripartite correlations. Interestingly, entanglement dark periods can enable plateaux of nonzero tripartite correlations. We then explain this behavior in terms of information flows among the different parties of the system. Besides showcasing the phenomenon of the freezing of overall correlations, our results provide insights on the origin of retrieval of entanglement within a hybrid quantum-classical system.

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“…Proof. Condition (1 − α 2 )(1 − s ∞ 0 λ k (t)e −st dt) < 1 guarantees the validity of expansion (16). Let Φ(t) be nonpositive.…”

Section: The Class Of Commutative Hermitian Dynamical Maps Comprises mentioning

confidence: 99%

“…Let us consider a qubit evolution where the rescaling of the memory kernel is compatible with P divisibility of the dynamical map. Following [16], let Φ(t) be a Pauli qubit dynamical map governed by the memory kernel…”

Section: The Class Of Commutative Hermitian Dynamical Maps Comprises mentioning

confidence: 99%

Time deformations of master equations

Filippov

Chruściński

2018

Phys. Rev. A

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Convolutionless and convolution master equations are the two mostly used physical descriptions of open quantum systems dynamics. We subject these equations to time deformations: local dilations and contractions of time scale. We prove that the convolutionless equation remains legitimate under any time deformation (results in a completely positive dynamical map) if and only if the original dynamics is completely positive divisible. Similarly, for a specific class of convolution master equations we show that uniform time dilations preserve positivity of the deformed map if the original map is positive divisible. These results allow witnessing different types of non-Markovian behavior: the absence of complete positivity for a deformed convolutionless master equation clearly indicates that the original dynamics is at least weakly non-Markovian; the absence of positivity for a class of time-dilated convolution master equations is a witness of essentially non-Markovian original dynamics.

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Admissible memory kernels for random unitary qubit evolution

Cited by 36 publications

References 48 publications

Mixing-induced quantum non-Markovianity and information flow

Mixing-induced quantum non-Markovianity and information flow

Distributed correlations and information flows within a hybrid multipartite quantum-classical system

Time deformations of master equations

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