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Journal of Modern Optics

Stationary discord and non-local correlations via qubit damping

A.‐S. F. Obada, H. A. Hessian, A.‐B. A. Mohamed, Mostafa Hashem

Published Mar 16, 2015• 6 citations
Publisher

Abstract

By using quantum discord (QD), measurement induced non-locality (MIN) and negativity (QE), quantum correlation and entanglement are investigated for two qubits in two different cases for the initial two qubit Werner states, taking into account the influence of qubit damping. It is shown that there is no asymptotic decay for MIN while asymptotic decay exists for QD and QE. Quantum correlations cannot be strengthened by introducing the damping. The appearance time of stationary correlations gets shorter with the increase in the damping parameter. Finally, a uniform damping qubit can affect the stationary correlations when the qubits are initially in an entangled state.

DOI
10.1080/09500340.2015.1015637

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By using quantum discord (QD), measurement induced non-locality (MIN) and negativity (QE), quantum correlation and entanglement are investigated for two qubits in two different cases for the initial two qubit Werner states, taking into account the influence of qubit damping. It is shown that there is no asymptotic decay for MIN while asymptotic decay exists for QD and QE. Quantum correlations cannot be strengthened by introducing the damping. The appearance time of stationary correlations gets shorter with the increase in the damping parameter. Finally, a uniform damping qubit can affect the stationary correlations when the qubits are initially in an entangled state.
A system consists of two charged qubits are initially prepared in a maximum entangled Bell state and having no mutual interaction, where each qubit interacts independently with a superconducting transmission line resonator. An analytical solution of the time evolution of the final state of the system with the effect of a phase decoherence is found. In previous works, quantum correlations are only investigated in X-state for the models which are as our model. In this work, the analytical formulas of the geometric quantum discord (GQD) and measurement-induced non-locality (MIN) are introduced for a general state of two-qubit (non-X-state). Quantum correlations are studied via GQD and MIN with quantum entanglement (QE). It is found that a sudden disappearance only occurs for QE, while MIN and GQD still exist. Due to the increase in the amplitude of the coherent states, the intervals of the sudden disappearance of QE increase and MIN and GQD decrease. It is interesting to note that initial correlations can be lost and they reach their stationary correlations with the increase in the intrinsic decoherence. The stationary correlation of MIN can be destroyed, it reach zero value, when both the decoherence effect and detuning are present simultaneously. By starting with different types of Bell-like states, the stationary correlations as well as the time intervals of sudden disappearance have notable changes. It is possible to control the quantum correlations with certain parameter sets.
Abstract Quantum correlations in two superconducting (SC) qubits, placed in an SC-cavity and driven by noise fields, are investigated by using quantum discord (QD) and measurement-induced nonlocality with quantum entanglement (QE). It was found that the initial values of QD and measurement-induced non-locality (MIN) grow from zero-values to non-zero values. This growth of quantum correlations is due to the unitary qubits–field interaction. It is found that by increasing the coupling to the thermal environment, the generated correlations (of QD, MIN and QE) return to their zero-values and the phenomena of the sudden death and sudden birth only occur for QE. It is interesting to note that the state of two superconducting qubits has the quantum discord and quantum nonlocality without entanglement. The ability of the thermal field parameter for the disappearance of the generated correlations depend on the spontaneous emission parameter and vice versa.
Abstract It is known that the inevitable interaction of the entangled qubits with their environments may result in the degradation of quantum correlation. We study the decoherence of two remote qubits under general local single- and two-sided amplitude-damping channel (ADC). By using concurrence, quantum discord and Clauser–Horne–Shimony–Holt (CHSH) inequality, we find that the relation between the residual quantum correlations and the initial ones are different. Recently, Wang et al. [Int. J. Theor. Phys. 54 (2015) 5] showed that there exist a set of partially entangled states that are more robust than maximally entangled states in terms of the residual quantum correlation measured by concurrence, fully entangled fraction and quantum discord, respectively. Here we find that both in single- and two-sided ADC, only the evolution of CHSH inequality with the initial parameter is proportional to that of the initial nonlocality. That means the initial state with maximally nonlocality will retain its role in the evolution. It implies that the evolution of nonlocality may reveal the characteristics of quantum state better. Furthermore, we discuss the evolutions of the three different quantum measurements with the initial parameter under generalized amplitude damping channel (GADC) and find that they are all proportional to that of the initial state.
We show that two qubits, initially in a fully classical state, can develop significant quantum correlations as measured by the quantum discord (QD) under the action of a local memoryless noise (specifically we consider the case of a Markovian amplitude-damping channel). This is analytically proven after deriving in a compact form the QD for the class of separable states involved in such a process. We provide a picture in the Bloch sphere that unambiguously highlights the physical mechanism behind the effect regardless of the specific measure of quantum correlations adopted.
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.
Time evolutions of quantum correlation, classical correlation and total correlation of two qubits are investigated when the two qubits are placed under the influence of classical phase fluctuations with correlation. Stochastic variables that describe the phase fluctuations are correlated and subject to the stationary Gauss–Markov process. The model includes the local and global dephasing models. It is shown that the quantum correlation measured by the quantum discord is increased by the correlation between the stochastic variables in the initial time region while the classical correlation and the total correlation are not. Furthermore the entanglement, the optimal fidelity of the quantum teleportation and the violation of the Bell inequality are investigated.