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Journal of the Optical Society of America B

Death and revival of the quantum discord and the measurement-induced disturbance

Miguel Gallego, Miguel Orszag

Published Jun 19, 2012• 3 citations
Publisher

Abstract

Three different quantifiers, entanglement of formation (ENT), quantum discord (QD), and measurement-induced disturbance (MID), are used to measure the quantum correlations of two qubits in a common squeezed bath. A subspace was found for initial conditions in a squeezed bath, where the system experiences no decoherence. We relate the three measurements with the “distance” from the initial condition to the decoherence free subspace, in order to study the effect of the decoherence in the quantum correlations. We show examples of a system with quantum correlations even when entanglement is null. Furthermore, we study the necessary conditions for the system to become truly classical. We found that, under certain initial conditions and at specific times, the system becomes classical and both the QD and the MID vanish, thus observing the phenomena of sudden death and revival of the quantum correlations. Finally, we observe discontinuities in the QD.

DOI
10.1364/josab.29.001690

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Three different quantifiers, entanglement of formation (ENT), quantum discord (QD), and measurement-induced disturbance (MID), are used to measure the quantum correlations of two qubits in a common squeezed bath. A subspace was found for initial conditions in a squeezed bath, where the system experiences no decoherence. We relate the three measurements with the “distance” from the initial condition to the decoherence free subspace, in order to study the effect of the decoherence in the quantum correlations. We show examples of a system with quantum correlations even when entanglement is null. Furthermore, we study the necessary conditions for the system to become truly classical. We found that, under certain initial conditions and at specific times, the system becomes classical and both the QD and the MID vanish, thus observing the phenomena of sudden death and revival of the quantum correlations. Finally, we observe discontinuities in the QD.
"or many years the entangled systems have been associated to the quantum world, while the separable systems with the classical world. Recently quantum discord showed that some separable states posses quantum correlation even when the entanglement is zero. In this work, we compare different features of quantum discord and entanglement of formation for two qubits in a common squeezed reservoir. We relate the quantum correlations with the “distance” of our initial condition from the decoherence free subspace where the system is not affected by environment. While for some initial conditions, the entanglement presents sudden death and revival, quantum discord does not. Still, is not clear the relation between these two measurements of “quantumness”."
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.
Correlations in open quantum systems exhibit peculiar phenomena under the effect of various sources of noise. Here, we investigate the dynamics of entanglement and quantum discord (QD) for three noninteracting qubits coupled with a classical environmental static noise characterized by an external random field. Two initial entangled states of the system are examined, namely, the GHZ- and [Formula: see text]-type states. The system-environment interaction is here analyzed in three different configurations, namely, independent, mixed and common environments. We find that the dynamics of quantum correlations are strongly affected by the type of system-environment interaction and the purity of the initial entangled state. Indeed, depending on the type of interaction and the value of the purity of the initial state, peculiar phenomena such as sudden death, revivals and long-time survival of quantum correlations are observed. On the other hand, our results clearly show that quantum correlations initially present in the [Formula: see text]-type states are less robust than those of the GHZ-type states. Furthermore, we find that the long-time survival of entanglement can be detected by means of the suitable entanglement witnesses.
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.
Decoherence arises from the interaction of a quantum system with the environment or, more precisely, from the measurement in which the environment ``measures'' the quantum system and establishes correlations with it. In this work, we first quantify measurement-induced correlations from both classical and quantum perspectives. Then we quantify decoherence via measurement-induced classical correlations. By virtue of an intrinsic and powerful link between entanglement (as quantified by entanglement of formation) and classical correlations (as quantified by the difference between the total correlations and quantum discord) in pure tripartite systems, we present general analytical formulas for measurement-induced correlations and decoherence measures for qubit systems and, furthermore, reveal a conservation relation for the information-disturbance tradeoff.
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.