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Quantum Information and Computation

Quantum discord of a three-qubit W-class state in noisy environments

Hui Guo, Jin‐Ming Liu, Chengjie Zhang, C. H. Oh

Published Jul 1, 2012• 7 citations
Publisher

Abstract

We study the dynamics of the pairwise quantum discord (QD), classical correlation (CC), and entanglement of formation (EOF) for the three-qubit W-class state |W>_{123}=\frac 12(|100>_{123}+|010>_{123}+\sqrt{2}|001>_{123}) under the influence of various Markovian noises by analytically solving the master equation in the Lindblad form. Through numerical analysis, we find that EOF decreases asymptotically to zero with time for the dephasing noise, but it undergoes sudden death for the bit-flip noise, the isotropic noise, as well as the dissipative and noisy environments. Moreover, QD decays to zero in an asymptotical way for all the noises we investigated. Thus, when the W-class state |W>_{123} is subject to the above Markovian noises, QD is more robust than EOF against decoherence excluding the phase-flip noise, implying that QD is more useful than entanglement to characterize the quantum correlation. We also find a remarkable character for the CC in the presence of the phase-flip noise, i.e., CC displays the behavior of sudden transition and then keeps constant permanently, but the corresponding QD just exhibits a very small sudden change. Furthermore, we verify the monogamic relation between the pairwise QD and EOF of the W-class state.

DOI
10.26421/qic12.7-8-12

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We study the dynamics of the pairwise quantum discord (QD), classical correlation (CC), and entanglement of formation (EOF) for the three-qubit W-class state |W>{123}=\frac 12(|100>{123}+|010>{123}+\sqrt{2}|001>{123}) under the influence of various Markovian noises by analytically solving the master equation in the Lindblad form. Through numerical analysis, we find that EOF decreases asymptotically to zero with time for the dephasing noise, but it undergoes sudden death for the bit-flip noise, the isotropic noise, as well as the dissipative and noisy environments. Moreover, QD decays to zero in an asymptotical way for all the noises we investigated. Thus, when the W-class state |W>_{123} is subject to the above Markovian noises, QD is more robust than EOF against decoherence excluding the phase-flip noise, implying that QD is more useful than entanglement to characterize the quantum correlation. We also find a remarkable character for the CC in the presence of the phase-flip noise, i.e., CC displays the behavior of sudden transition and then keeps constant permanently, but the corresponding QD just exhibits a very small sudden change. Furthermore, we verify the monogamic relation between the pairwise QD and EOF of the W-class state.
We address the effect of classical noise on the dynamics of quantum correlations, entanglement and quantum discord (QD), of two non-interacting qubits initially prepared in a Bell state. The effect of noise is modeled by randomizing the single-qubit transition amplitudes. We address both static and dynamic environmental noise corresponding to interaction with separate and common baths in either Markovian and non-Markovian regimes. In the Markov regime, a monotone decay of the quantum correlations is found, whereas for non-Markovian noise sudden death and revival phenomena may occur, depending on the characteristics of the noise. Entanglement and QD show the same qualitative behavior for all kind of noises considered. On the other hand, we find that separate and common environments may play opposite roles in preserving quantum correlations, depending on the noise regime considered.
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.
We study the dynamics of quantum dissension for three qubit states in various dissipative channels such as amplitude damping, dephasing and depolarizing. Our study is solely based on Markovian environments where quantum channels are without memory and each qubit is coupled to its own environment. We start with mixed GHZ, mixed W, mixture of separable states, a mixed biseparable state, as the initial states and mostly observe that the decay of quantum dissension is asymptotic in contrast to sudden death of quantum entanglement in similar environments. This is a clear indication of the fact that quantum correlation in general is more robust against the effect of noise. However, for a given class of initial mixed states we find a temporary leap in quantum dissension for a certain interval of time. More precisely, we observe the revival of quantum correlation to happen for certain time period. This signifies that the measure of quantum correlation such as quantum discord, quantum dissension, defined from the information theoretic perspective is different from the correlation defined from the entanglement-separability paradigm and can increase under the effect of the local noise. We also study the effects of these channels on the monogamy score of each of these initial states. Interestingly, we find that for certain class of states and channels, there is change from negative values to positive values of the monogamy score with classical randomness as well as with time. This gives us an important insight in obtaining states which are freely sharable (polygamous state) from the states which are not freely sharable (monogamous). This is indeed a remarkable feature, as we can create monogamous states from polygamous states Monogamous states are considered to have more signatures of quantum ness and can be used for security purpose.
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.
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.
We calculate the dissipative dynamics of two-qubit quantum discord under Markovian environments. We analyze various dissipative channels such as dephasing, depolarizing, and generalized amplitude damping, assuming independent perturbation, in which each qubit is coupled to its own channel. Choosing initial conditions that manifest the so-called sudden death of entanglement, we compare the dynamics of entanglement with that of quantum discord. We show that in all cases where entanglement suddenly disappears, quantum discord vanishes only in the asymptotic limit, behaving similarly to individual decoherence of the qubits, even at finite temperatures. Hence, quantum discord is more robust than the entanglement against decoherence so that quantum algorithms based only on quantum discord correlations may be more robust than those based on entanglement.