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Communications in Theoretical Physics

Dynamics of Super Quantum Correlations and Quantum Correlations for a System of Three Qubits

Fatima-Zahra Siyouri, M. El Baz, Saad Rfifi, Y. Hassouni

Published Apr 1, 2016• 9 citations
Publisher

Abstract

Abstract The dynamics of quantum discord for two qubits independently interacting with dephasing reservoirs have been studied recently. The authors [Phys. Rev. A 88 (2013) 034304] found that for some Bell-diagonal states (BDS) which interact with their environments the calculation of quantum discord could experience a sudden transition in its dynamics, this phenomenon is known as the sudden change. Here in the present paper, we analyze the dynamics of normal quantum discord and super quantum discord for tripartite Bell-diagonal states independently interacting with dephasing reservoirs. Then, we find that basis change does not necessary mean sudden change of quantum correlations.

DOI
10.1088/0253-6102/65/4/447

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Abstract The dynamics of quantum discord for two qubits independently interacting with dephasing reservoirs have been studied recently. The authors [Phys. Rev. A 88 (2013) 034304] found that for some Bell-diagonal states (BDS) which interact with their environments the calculation of quantum discord could experience a sudden transition in its dynamics, this phenomenon is known as the sudden change. Here in the present paper, we analyze the dynamics of normal quantum discord and super quantum discord for tripartite Bell-diagonal states independently interacting with dephasing reservoirs. Then, we find that basis change does not necessary mean sudden change of quantum correlations.
It is known that quantum discord might experience a sudden transition in its dynamics when calculated for certain Bell-diagonal states (BDS) that are in interaction with their surroundings. We examine this phenomenon, known as the sudden change of quantum discord, considering the case of two qubits independently interacting with dephasing reservoirs. We first demonstrate that, for a class of initial states which can be chosen arbitrarily close to BDS, the transition is in fact not sudden, although it might numerically appear so if not studied carefully. Then, we provide an extension of this discussion covering the X\mathsf{X}X-shaped density matrices. Our findings suggest that the transition of quantum discord might be sudden only for an highly idealized zero-measure subset of states within the set of all possible initial conditions of two qubits.
In this work, we study the dynamics of quantum correlation (QC) in terms of quantum discord and its transfer for multiqubit systems in dissipative environments. At first, we investigate the dynamics of bipartite QC contained in a three-qubit system that are initially prepared in an extended W-like state with each qubit coupled to an independent reservoir. Subsequently, we study a realistic quantum network of several remote nodes each of which contains two qubits in contact with a common reservoir. For the simplest case of two nodes, we study the dynamics of QC and its transfer from the initially correlated system to the reservoirs and other degrees of freedom. In both models, we pay particular attention to the independent evolution and transfer of QC without the participation of entanglement when the systems of interest are initially prepared in unentangled states. We also observe the occurrence of sudden changes of quantum discord when the systems are initially in mixed states.
The dynamics of classical correlation and quantum correlation of two qubits in an independent and common dissipative cavity are studied. We show that for an independent case, the quantum correlation keeps constant and the correlation relation decays before the critical time point Ωt¯. On the other hand t>Ωt¯, for the classical correlation does not change and the quantum correlation is lost. These situations demonstrate that the phenomenon of sudden transition between classical and quantum decoherence appears during the time evolution. For the common case, the quantum correlation dynamics is quite different. It is displayed that for some initial states, the quantum correlation can increase up to the critical point of time, after which it decreases, which means that the quantum correlation presents a sudden change of behavior in their decay rates. But for other initial states, the quantum correlation can keep increasing up to some-steady state value. Furthermore, we also investigate the nonzero quantum correlation between two qubits induced by the dissipation of the cavity.
We study the peculiar dynamics of two qubits quantum discord with a sudden change in behavior. It is widely agreed in the literature nowadays that environment induce sudden change behavior of quantum discord. We explore the sudden change phenomenon under the action of local-independent environments, considering the discord of two-qubit which is obtained by means of the weak measurements on one of the two-qubit. It is shown that the sudden change phenomenon does not appear under weak measurements. We find that the quantum discord with weak measurements decays in a monotonic fashion, and show that quantum discord might exhibit a sudden change only for the strong (projective) measurement. We believe that environment is not the main role of the sudden change, but the quantum correlation itself is.
We evaluate the quantum discord dynamics of two qubits in independent and common non-Markovian environments. We compare the dynamics of entanglement with that of quantum discord. For independent reservoirs the quantum discord vanishes only at discrete instants whereas the entanglement can disappear during a finite time interval. For a common reservoir, quantum discord and entanglement can behave very differently with sudden birth of the former but not of the latter. Furthermore, in this case the quantum discord dynamics presents sudden changes in the derivative of its time evolution which is evidenced by the presence of kinks in its behavior at discrete instants of time.
We study the quantum discord dynamics of a bipartite composite system in the presence of a dissipative environment and investigate the effect of the interaction between the two subsystems. The results show that the interaction can influence the sudden transition between the quantum correlation and the classical correlation and for the maximally mixed marginals initial states, the sudden transition regime will always exist. The entanglements are also discussed in comparison to the quantum discord in describing the quantum correlations.