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Laser Physics

Trace distance discord and Bell-function correlations beyond entanglement in two SC-qubits interacting with a dissipative SC-cavity

A.‐S. F. Obada, A-B A Mohamed, Mostafa Hashem, M M Elkhateeb

Published Apr 28, 2020• 6 citations
Publisher

Abstract

Abstract An analytical solution for the dissipative system of two charge qubits located in an SC-cavity field is obtained in the dispersive regime. Therefore, the quantum correlation of the trace distance discord, the Bell function and the logarithmic negativity are investigated. The sensitivity of the correlation measures are investigated under the physical parameters of the phase damping and the qubit distribution angle of the initial symmetric/non-symmetric Bell-state, whereby correlation phenomena, such as the oscillatory behavior, disappearance/appearance and the collapses/revivals, are proven to demonstrate noticeable changes and high sensitivity to these physical parameters. It is shown that the unitary cavity-qubit interaction leads to the generation of quantum correlations periodically with different amplitudes and oscillations which depend on the initial two-qubit state and its distribution angle. The increase of the two-qubit phase damping leads to the complete disappearance of the generated trace distance, Bell function and log-negativity correlations.

DOI
10.1088/1555-6611/ab7f38

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Abstract An analytical solution for the dissipative system of two charge qubits located in an SC-cavity field is obtained in the dispersive regime. Therefore, the quantum correlation of the trace distance discord, the Bell function and the logarithmic negativity are investigated. The sensitivity of the correlation measures are investigated under the physical parameters of the phase damping and the qubit distribution angle of the initial symmetric/non-symmetric Bell-state, whereby correlation phenomena, such as the oscillatory behavior, disappearance/appearance and the collapses/revivals, are proven to demonstrate noticeable changes and high sensitivity to these physical parameters. It is shown that the unitary cavity-qubit interaction leads to the generation of quantum correlations periodically with different amplitudes and oscillations which depend on the initial two-qubit state and its distribution angle. The increase of the two-qubit phase damping leads to the complete disappearance of the generated trace distance, Bell function and log-negativity correlations.
We study the time evolution of three quantifiers of nonclassical correlations, namely uncertainty-induced nonlocality (UIN), trace distance discord (TDD), and logarithmic negativity (LN), in a hybrid spin–cavity system with anisotropic XY interactions and two-photon spin-field coupling. We examine how the interaction parameters, including the anisotropy strength, initial photon number, spin–cavity coupling, spin–spin interaction, and spin–cavity detuning, influence the resulting two-qubit correlations. Our results show that both spin–cavity and spin–spin couplings can efficiently generate UIN, TDD, and entanglement, each exhibiting distinct oscillatory features, and we further evaluate the robustness of these features as the other interaction parameters increase. In the presence of cavity dissipation and spontaneous emission, entanglement is rapidly suppressed and may undergo entanglement sudden death, whereas UIN and TDD remain noticeably nonzero over longer times despite the damping of their oscillations. Overall, our findings provide a comparative characterization of entanglement and discord-like correlations in a dissipative spin–cavity platform and highlight the greater persistence of UIN- and TDD-type correlations within the present dissipative framework.
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.
In this paper, we explore distribution dynamics of two-qubit Fisher and skew information correlations of a dissipative microwave cavity field interacting with two charged superconducting qubits. Besides the negativity function, non-classical correlations beyond entanglement are studied using local quantum Fisher information (LQFI) and local quantum uncertainty (LQU). We find that the two-qubit non-classical correlations are sensitive to qubit–qubit distribution angle, two-qubit dissipation parameter, and initial coherent state intensity. The phenomena of frozen quantum correlations, sudden death or birth, as well as revival dynamical maps are feasible in the current two-qubit state when exposed to a microwave cavity. The non-classical correlations and entanglement have been found damped under the two-qubit dissipation appearance in the field. For the increasing strength of coherence intensity of the field, the two-qubit non-classical correlations functions remain to emerge quickly and oscillate with higher frequency, although with the least amplitudes. Interestingly, unlike the non-classical correlations, negativity does not emerge against higher coherence strengths of the cavity and remains completely zero. Finally, for the least dissipation and higher coherence strength, one can readily generate non-classical two-qubit states employing a microwave cavity.
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.
We investigate the behavior of quantum correlations in some specific Werner-like two-qubit states, where the qubit interacts individually with non-Markovian environment. We employ the local quantum uncertainty and trace distance discord to quantify the amount of quantum correlations between the evolved qubits and the corresponding analytical expressions are derived. For specific values of the parameters characterizing the whole system, the dynamics of quantum correlations exhibits collapse and revival phenomena. The influence of the non-Markovianity is also investigated to analyze the monotonic decay of quantum correlations in the limiting case of Markovian regime. Furthermore, we show that trace distance discord captures quantum correlations that cannot be revealed by local quantum uncertainty in some particular situations.