Exact master equations for the non-Markovian decay of a qubit

Vacchini, Bassano; Breuer, Heinz‐Peter

doi:10.1103/physreva.81.042103

Cited by 129 publications

(143 citation statements)

References 40 publications

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“…Besides, we can see from Eqs. (16) and (17) that for a sufficiently high-temperature environment, i.e.,hω c k B T , the phase-damping factor, which is the main agent responsible for the decoherence, behaves as (t,T ) ≈ ηω T t, causing an exponential decay of the off-diagonal elements of the density operator. Moreover, as the phase factor (t) implies an oscillation with frequency ηω c , this time evolution is always slightly underdamped.…”

Section: Exact Dissipative Dynamicsmentioning

confidence: 99%

“…The state fidelity (24) will present an oscillatory behavior in the quantum regime (ω c ω T ), where the exponential decay factor (17) plays a minor role compared to the oscillatory factor (16), and the quantum vacuum fluctuations contribute predominantly. Although Eq.…”

Section: Fidelity Dynamics In An Mbqcmentioning

confidence: 99%

“…However, it is known that this interaction can result in nonmonotonical dynamics of the density-matrix coherences [10][11][12] and so a complete understanding of this behavior is a matter of great importance. Moreover, this nonmonotonical behavior is a subject of broad interest [13][14][15][16] since this peculiar property brings up unexpected dynamics for quantum fidelity [17], as well as for quantum entanglement [12,[18][19][20] and quantum discord [21]. When an open quantum system interacts with the outside world, there are two main effects that have to be considered: the relaxation and the decoherence processes.…”

Section: Introductionmentioning

confidence: 99%

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Exact dynamics of single-qubit-gate fidelities under the measurement-based quantum computation scheme

et al. 2012

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Measurement-based quantum computation is an efficient model to perform universal computation. Nevertheless, theoretical questions have been raised, mainly with respect to realistic noise conditions. In order to shed some light on this issue, we evaluate the exact dynamics of some single-qubit-gate fidelities using the measurement-based quantum computation scheme when the qubits which are used as a resource interact with a common dephasing environment. We report a necessary condition for the fidelity dynamics of a general pure N -qubit state, interacting with this type of error channel, to present an oscillatory behavior, and we show that for the initial canonical cluster state, the fidelity oscillates as a function of time. This state fidelity oscillatory behavior brings significant variations to the values of the computational results of a generic gate acting on that state depending on the instants we choose to apply our set of projective measurements. As we shall see, considering some specific gates that are frequently found in the literature, the fast application of the set of projective measurements does not necessarily imply high gate fidelity, and likewise the slow application thereof does not necessarily imply low gate fidelity. Our condition for the occurrence of the fidelity oscillatory behavior shows that the oscillation presented by the cluster state is due exclusively to its initial geometry. Other states that can be used as resources for measurement-based quantum computation can present the same initial geometrical condition. Therefore, it is very important for the present scheme to know when the fidelity of a particular resource state will oscillate in time and, if this is the case, what are the best times to perform the measurements.

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Section: Exact Dissipative Dynamicsmentioning

confidence: 99%

Section: Fidelity Dynamics In An Mbqcmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Exact dynamics of single-qubit-gate fidelities under the measurement-based quantum computation scheme

et al. 2012

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“…In the context, the general exponential memory kernel function is considered as f (t) = A exp(−γt) where A is the amplitude of the kernel and γ represents the memory decaying rate. This kind of memory kernel can be physically modeled by [30]. The definite expression of the matrix P can be obtained by…”

Section: The Completely Positive Reduced Dynamical Mapmentioning

confidence: 99%

Dynamics of Quantum Entanglement in Reservoir with Memory Effects

Hao

Sha

Sun

et al. 2012

Commun. Theor. Phys.

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The non-Markovian dynamics of quantum entanglement is studied by the Shabani-Lidar master equation when one of entangled quantum systems is coupled to a local reservoir with memory effects.The completely positive reduced dynamical map can be constructed in the Kraus representation.Quantum entanglement decays more slowly in the non-Markovian environment. The decoherence time for quantum entanglement can be markedly increased by the change of the memory kernel.It is found out that the entanglement sudden death between quantum systems and entanglement sudden birth between the system and reservoir occur at different instants.

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“…72,73,79 There are also numerous non-Markovian generalizations of the master equation. [80][81][82][83] In the above derivation it was assumed that the system is weakly coupled to the environment. Indeed, for practical purposes this is the most interesting case: if the coupling of the system to the environment is strong, the system behaves classically and can be described with classical equations of motion, while if the coupling is absent altogether, eqn (1) is valid.…”

Section: This Journal Is C the Owner Societies 2010mentioning

confidence: 99%

Single molecule charge transport: from a quantum mechanical to a classical description

Kocherzhenko

Grozema

Siebbeles

2011

Phys. Chem. Chem. Phys.

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This paper explores charge transport at the single molecule level. The conductive properties of both small organic molecules and conjugated polymers (molecular wires) are considered. In particular, the reasons for the transition from fully coherent to incoherent charge transport and the approaches that can be taken to describe this transition are addressed in some detail. The effects of molecular orbital symmetry, quantum interference, static disorder and molecular vibrations on charge transport are discussed. All of these effects must be taken into account (and may be used in a functional way) in the design of molecular electronic devices. An overview of the theoretical models employed when studying charge transport in small organic molecules and molecular wires is presented.

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Exact master equations for the non-Markovian decay of a qubit

Cited by 129 publications

References 40 publications

Exact dynamics of single-qubit-gate fidelities under the measurement-based quantum computation scheme

Exact dynamics of single-qubit-gate fidelities under the measurement-based quantum computation scheme

Dynamics of Quantum Entanglement in Reservoir with Memory Effects

Single molecule charge transport: from a quantum mechanical to a classical description

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