Single-qubit decoherence under a separable coupling to a random matrix environment

Carrera, M.; Gorin, T.; Seligman, T. H.

doi:10.1103/physreva.90.022107

Cited by 12 publications

(21 citation statements)

References 42 publications

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“…Besides, the above works focus mostly on the entanglement characteristics known as the purity and the fidelity, while we carry out the simultaneous comparative study of three entanglement characteristics: the concurrence, the negativity and the quantum discord, widely used in quantum information theory and allowing for the study of quite interesting quantum coherence phenomena. This makes essentially complementary the results of [23][24][25][26] and our results.…”

Section: Introductionsupporting

confidence: 90%

“…One has to choose then the time (the energy) scale of random matrix theory. We choose the socalled global regime which provides the description analogous to that of non-equilibrium statistical mechanics and the theory of open systems (see, however, works [23][24][25][26] for another choice known as the local regime, pertinent to the quantum chaos studies and leading to complementary results).…”

Section: Resultsmentioning

confidence: 99%

“…The quantum dynamics and their analysis in our work generalize those introduced in [21,22], where one qubit embedded into a 'random matrix' environment has been considered Note that the random matrix models of the dynamics of two qubits and of more general quantum systems embedded into an environment have been already considered, see e.g. [23][24][25][26] and references therein. The main difference between our work and the above works is that they are confined to the Heisenberg time scale pertinent for the quantum chaos studies, while in our work we deal with a shorter time scale commonly used in nonequilibrium statistical mechanics and the theory of open systems.…”

Section: Introductionmentioning

confidence: 91%

“…This is why [23][24][25] confine themselves to the first order approximation in the qubit-environment coupling for the reduced density matrix. The work [26] extends the result of [23][24][25] on an essentially larger interval of time and the system-environment interaction by using the Grassmann integration techniques but still remaining in the frameworks of the local regime, i.e., within the Heisenberg time scale t~N H . On the other hand, the global regime is fairly well understood and allow us to find closed expression for the reduced density matrix, applicable within the kinetics time scale.…”

Section: Two-qubit Random Matrix Hamiltoniansmentioning

confidence: 99%

“…Note that random matrices, in particular, Hamiltonians similar to our Hamiltonians (2.3)-(2.5), have been used in the description of the qubits dynamics, although in a more generic form which does not possesses the Pauli matrix structure, see [24][25][26] and references therein. The Pauli matrix structure of the one-qubit random matrix Hamiltonian (2.25) has been considered in [21] and later in [22,23,35].…”

Section: Two-qubit Random Matrix Hamiltoniansmentioning

confidence: 99%

See 4 more Smart Citations

On the qubits dynamics in random matrix environment

Bratus

Pastur

2018

J. Phys. Commun.

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We consider the entanglement evolution of two qubits embedded into disordered multiconnected environment. We model the environment and its interaction with qubits by large random matrices allowing for a possibility to describe environments of meso-and even nanosize. We obtain general formulas for the time dependent reduced density matrix of the qubits corresponding to several cases of the qubit-environment interaction and initial condition. We then workout an analog of BornMarkov approximation to find the evolution of the widely used entanglement quantifiers: the concurrence, the negativity and the quantum discord. We show that even in this approximation the time evolution of the reduced density matrix can be non-Markovian, thereby describing certain memory effects due to the backaction of the environment on qubits. In particular, we find the vanishing of the entanglement at finite moments and its subsequent revivals (entanglement sudden death and entanglement sudden birth). Our results, partly known and partly new, can be viewed as a manifestation of the universality of certain properties of decoherent qubit evolution which have been found previously in various versions of bosonic macroscopic environment.

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Section: Introductionsupporting

confidence: 90%

Section: Resultsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 91%

Section: Two-qubit Random Matrix Hamiltoniansmentioning

confidence: 99%

Section: Two-qubit Random Matrix Hamiltoniansmentioning

confidence: 99%

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On the qubits dynamics in random matrix environment

Bratus

Pastur

2018

J. Phys. Commun.

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Random density matrices versus random evolution of open system

Pineda¹,

Seligman²

2015

J. Phys. A: Math. Theor.

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We present and compare two families of ensembles of random density matrices. The first, static ensemble, is obtained foliating an unbiased ensemble of density matrices. As criterion we use fixed purity as the simplest example of a useful convex function. The second, dynamic ensemble, is inspired in random matrix models for decoherence where one evolves a separable pure state with a random Hamiltonian until a given value of purity in the central system is achieved. Several families of Hamiltonians, adequate for different physical situations, are studied. We focus on a two qubit central system, and obtain exact expressions for the static case. The ensemble displays a peak around Werner-like states, modulated by nodes on the degeneracies of the density matrices. For moderate and strong interactions good agreement between the static and the dynamic ensembles is found. Even in a model where one qubit does not interact with the environment excellent agreement is found, but only if there is maximal entanglement with the interacting one. The discussion is started recalling similar considerations for scattering theory. At the end, we comment on the reach of the results for other convex functions of the density matrix, and exemplify the situation with the von Neumann entropy.

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Markovian and non-Markovian dynamics induced by a generic environment

2019

Self Cite

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We study the open dynamics of a quantum two-level system coupled to an environment modeled by random matrices. Using the quantum channel formalism, we investigate different quantum Markovianity measures and criteria. A thorough analysis of the whole parameter space, reveals a wide range of different regimes, ranging from strongly non-Markovian to Markovian dynamics. In contrast to analytical models, all non-Markovianity measures and criteria have to be applied to data with fluctuations and statistical uncertainties. We discuss the practical usefulness of the different approaches.

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Single-qubit decoherence under a separable coupling to a random matrix environment

Cited by 12 publications

References 42 publications

On the qubits dynamics in random matrix environment

On the qubits dynamics in random matrix environment

Random density matrices versus random evolution of open system

Markovian and non-Markovian dynamics induced by a generic environment

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