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Laser Physics

Investigation of quantum and classical correlations in a quantum dot system under decoherence

K. Berrada

Published Aug 6, 2013• 3 citations
Publisher

Abstract

In this paper, we investigate quantitatively the thermal classical and quantum correlations in an isolated quantum dot system (QDS) including the effects of different parameters. We show that the quantum discord (QD) is more resistant against the temperature effect and might be finite even for higher temperatures in the asymptotic limit. Decoherence in a QDS caused by interaction with its environment is another interesting issue in the quantum information field. Assuming Markovian dynamics for the time evolution, we present noise models for the QDS by using Kraus operators for several noisy channels; in particular bit flip, bit-phase flip, phase flip, and depolarizing channels. By analytical and numerical analyses, we investigate the dynamics of different kinds of correlations, namely, the mutual information, the classical correlation, the entanglement of formation (EOF), and the QD in different channels. The sudden change in behavior in the decay rates of correlations and their immunity against certain decoherences are shown. We explore a symmetry among these channels and provide the decoherence areas for which both classical and quantum correlations remain affected in the QDS.

DOI
10.1088/1054-660x/23/9/095201

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In this paper, we investigate quantitatively the thermal classical and quantum correlations in an isolated quantum dot system (QDS) including the effects of different parameters. We show that the quantum discord (QD) is more resistant against the temperature effect and might be finite even for higher temperatures in the asymptotic limit. Decoherence in a QDS caused by interaction with its environment is another interesting issue in the quantum information field. Assuming Markovian dynamics for the time evolution, we present noise models for the QDS by using Kraus operators for several noisy channels; in particular bit flip, bit-phase flip, phase flip, and depolarizing channels. By analytical and numerical analyses, we investigate the dynamics of different kinds of correlations, namely, the mutual information, the classical correlation, the entanglement of formation (EOF), and the QD in different channels. The sudden change in behavior in the decay rates of correlations and their immunity against certain decoherences are shown. We explore a symmetry among these channels and provide the decoherence areas for which both classical and quantum correlations remain affected in the QDS.
The non-Markovian decoherence of quantum and classical correlations is analytically obtained when two qubits are asymmetrically subjected to the bit flip channel and phase flip channel. For one class of initial mixed states, quantum correlations quantified by quantum discord decay synchronously with classical correlations. The discovery that the decaying rates of quantum and classical correlations suddenly change at the characteristic time is physically interpreted by the distance from quantum state to the closest classical states. In a large time interval, quantum correlations are greater than classical correlations. The quantum and classical correlations can be preserved over a longer period of time via the kernel characterizing the environment memory effects.
Quantum discord is a more general measure of quantum correlations than entanglement and has been proposed as a resource in certain quantum information processing tasks. The computation of discord is mostly confined to two-qubit systems for which an analytical calculational scheme is available. The utilization of quantum correlations in quantum information-based applications is limited by the problem of decoherence, i.e., the loss of coherence due to the inevitable interaction of a quantum system with its environment. The dynamics of quantum correlations due to decoherence may be studied in the Kraus operator formalism for different types of quantum channels representing system-environment interactions. In this review, we describe the salient features of the dynamics of classical and quantum correlations in a two-qubit system under Markovian (memoryless) time evolution. The two-qubit state considered is described by the reduced density matrix obtained from the ground state of a spin model. The models considered include the transverse-field XY model in one dimension, a special case of which is the transverse-field Ising model, and the XXZ spin chain. The quantum channels studied include the amplitude damping, bit-flip, bit-phase-flip and phase-flip channels. The Kraus operator formalism is briefly introduced and the origins of different types of dynamics discussed. One can identify appropriate quantities associated with the dynamics of quantum correlations which provide signatures of quantum phase transitions in the spin models. Experimental observations of the different types of dynamics are also mentioned.
The decoherence of quantum correlation is investigated in the Heisenberg spin system with the asymmetric anisotropic interactions. The quantum entanglement and discord are used to quantify the quantumness of the correlations. By the analytical and numerical methods, we find that quantum discord decays asymptotically in time under the effects of the independent local Markovian reservoirs. This is markedly different from the sudden change of the entanglement. Before the disappearance of the entanglement, the dynamic behaviour of quantum discord is very similar to that of the entanglement. It is also shown that the discord declines rapidly for the interacting spin system compared with the case of noninteracting qubits. At an arbitrary finite temperature, the nonzero thermal discord can be enhanced by the asymmetric anisotropic interactions which induce quantum fluctuations.
We study the dynamics of quantum correlations of two coupled double quantum dots containing two excess electrons. The dissipation is included through the contact with an oscillator bath. We solve the Redfield master equation in order to determine the dynamics of the quantum discord (QD) and the entanglement of formation (EoF). Based on our results, we find that the QD is more resistant to dissipation than the EoF for such a system. We observe that this characteristic is related to whether the oscillator bath is common to both qubits or not and to the form of the interaction Hamiltonian. Moreover, our results show that the QD might be finite, even for higher temperatures in the asymptotic limit.
We investigate the quantum correlations in an axially symmetric hybrid qubit-qutrit system subjected to different noisy environments. We first introduce a physical model and analyze its Hamiltonian structure, emphasizing the role of hybrid dimensionality and axial symmetry. The effects of decoherence are then examined under two local noise mechanisms, namely dephasing and phase-flip channels, acting on the qubit and qutrit subsystems in both symmetric and asymmetric configurations. Quantum correlations are quantified using negativity to capture entanglement and quantum discord based on linear entropy to characterize more general nonclassical correlations. Our results show that both thermal fluctuations and phase noise lead to a monotonic degradation of quantum correlations, with increasing temperature accelerating coherence loss and inducing entanglement sudden death at finite temperatures. While negativity vanishes abruptly under sufficiently strong noise, quantum discord persists beyond the entanglement threshold, revealing residual quantum correlations in mixed states. We further demonstrate that asymmetric noise configurations significantly enhance the robustness of both entanglement and discord by partially shielding coherence in the less affected subsystem. A comparative analysis reveals that phase-flip noise is more destructive than pure dephasing, leading to faster suppression of quantum correlations.
The dissipative dynamics of classical correlation(CC), quantum discord(QD) and entanglement (QE) of two qubits in two-side and one-side decoherence models are inves- tigated under Markovian environments. We find the sudden change QD as well as CC and sudden death of entanglement (ESD). The results show that QD and QE decay faster with the increasing of squeezing parameter r; the dipole-dipole interaction W under two-side decoherence leads to the oscillation of quantum discord and concurrence for initial non- eigenstates; while in all cases when entanglement suddenly disappears, quantum discord keeps nonzero under same conditions.