Trace distance in stochastic dephasing with initial correlation

Ban, Masashi; Kitajima, Sachiko; Shibata, Fumiaki

doi:10.1103/physreva.84.042115

Cited by 8 publications

(8 citation statements)

References 18 publications

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“…They found that the growth of the quantum trace distance is closely related to the enhancement of the coherence. In the same way as stochastic dephasing, Ban et al [35] obtained the same conclusions. However, these conclusions are not always physically justified outside the weak-coupling interaction.…”

Section: Introductionmentioning

confidence: 61%

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Influences of counter-rotating wave terms on the trace distance of quantum states in the Rabi model

Deng

2013

J. Phys. B: At. Mol. Opt. Phys.

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Based on a unitary transformation and a generalized rotating-wave approximation, the effect of the counter-rotating wave terms on the trace distance of quantum states for the qubit in the Rabi model is investigated. The analytical expressions of the eigenenergies and eigenstates of the qubit–field coupling system are obtained approximately. Starting from the two initial Bell states for the qubit and field, in which the qubit is in the same states, we find that the time evolution of the trace distance for the qubit states is only related to the difference between the populations in the qubit excited state but independent of the coherence of the qubit. The effect of the counter-rotating wave terms brings the trace distance of the quantum states of the qubit to exhibit fast oscillations in the strong coupling regime.

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Section: Introductionmentioning

confidence: 61%

“…If the two quantum states are the qubit states, then the corresponding quantum trace distance reads [33,35]…”

Section: Dynamics Of the Quantum Trace Distancementioning

confidence: 99%

Influences of counter-rotating wave terms on the trace distance of quantum states in the Rabi model

Deng

2013

J. Phys. B: At. Mol. Opt. Phys.

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“…For initial conditions other than these, there is a possibility that the reduced dynamics may not be completely positive. Thus, for the reduced dynamics of open quantum systems, we have mutually related problems of the complete positivity, the Markovian versus non-Markovian property (non-Markovianity) and the correlated initial conditions [32,34,[41][42][43][44][45][46][47][48][49][50][51][52][53][54][55][56][57][58].…”

Section: Introductionmentioning

confidence: 99%

A solvable dissipative Jaynes–Cummings model with initial correlation

Kitajima¹,

Ban²,

Shibata³

2013

J. Phys. B: At. Mol. Opt. Phys.

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Dissipative properties of a composite system interacting with an environment are studied in order to obtain insight into relaxation and decoherence phenomena. As a typical system with internal degree of freedom, a Jaynes–Cummings (JC) model is considered where a spin (qubit) interacts with a single bosonic mode. When the whole system is initially in a state of at most single excitation, the model becomes solvable for excitation number conserving Hamiltonians, even if the JC system interacts with its environment composed of harmonic oscillators. Effects of initial correlations between the system and the environment are also taken into account. Basic equations for the density matrix are solved exactly to determine dynamics of the reduced systems. Mutually related problems of initial correlations, entanglement and non-Markovian property are studied explicitly by examining the time evolution of the reduced density matrices, the concurrence and the trace distance.

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“…The effects of initial system-environment correlations have been discussed regarding quantum measurements [12][13][14][15][16][17][18][19][20][21][22][23][24], complete positivity of dynamical maps [25][26][27][28][29][30][31], non-Markovian dynamics [32][33][34], linear-response absorption line shapes [35][36][37], and general theoretical treatments using the projection operator methods [38]. Especially relevant has been the finding that initial system-environment correlations require extension of the conceptual framework of open system reduced dynamics to include generalization of contractivity [39].…”

Section: Introductionmentioning

confidence: 99%

Exploring initial correlations in a Gibbs state by application of external field

Uchiyama

2012

Phys. Rev. A

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We demonstrate that local application of a weak external field increases distinguishability between states with and without initial correlations. We consider the case where a two-level system linearly and adiabatically interacts with an infinite number of bosons. We evaluate the trace distance (or, equivalently, the Hilbert-Schmidt distance) between the quantum states which evolve from two kinds of initial states; the correlated Gibbs state and its uncorrelated marginal state. We find that the trace distance increases above its initial value for any and all parameter settings. This indicates that we can explore the existence of initial system-environment correlations with applying a local external field, which causes the breakdown of the contractivity.

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Trace distance in stochastic dephasing with initial correlation

Cited by 8 publications

References 18 publications

Influences of counter-rotating wave terms on the trace distance of quantum states in the Rabi model

Influences of counter-rotating wave terms on the trace distance of quantum states in the Rabi model

A solvable dissipative Jaynes–Cummings model with initial correlation

Exploring initial correlations in a Gibbs state by application of external field

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