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Journal of Modern Optics

Non-classicality of two superconducting-qubits interacting independently with a resonator cavity: trace-norm correlation and Bures-distance entanglement

A.‐B. A. Mohamed, H. A. Hessian

Published Jan 2, 2021• 5 citations
Publisher

Abstract

We study the behaviour of the correlation robustness of two spatially isolated charge-qubits started initially with a maximally correlated nonsymmetric Bell-state. Each charged qubit is coupled individually to a superconducting resonator coherent field. The dynamics of the qubit-resonator quantum correlations, based on trace-norm measurement-induced non-locality (MIN) and Bures distance entanglement, are investigated under the effects of the qubit-resonator interactions, intrinsic decoherence, initial coherent intensity cavity as well as of the qubit-resonator detuning. It is found that the trace-norm MIN correlation can be enhanced by the initial coherent field intensity and the detuning. The MIN is more robust, against the qubit-resonator interactions and the decoherence, than the Bures distance entanglement. Furthermore, the correlation robustness analysed for the different cases of the coherent states depends not only on the intrinsic decoherence but also on the coherent states and the qubit-resonator detuning.

DOI
10.1080/09500340.2021.1872726

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We analytically investigate two separated qubits inside an open cavity field. The cavity is initially prepared in a superposition coherent state. The non-locality correlations [including trace norm measurement induced non-locality, maximal Bell-correlation, and concurrence entanglement] of the two qubits are explored. It is shown that, the generated non-locality correlations crucially depend on the decay and the initial coherence intensity of the cavity field. The enhancement of the initial coherence intensity and its superposition leads to increasing the generated non-locality correlations. The phenomena of sudden birth and death entanglement are found.
Abstract In this paper, we study the dynamics of two coupled qubits interacting with a two-mode parametric amplifier cavity through the nonlinear interactions of the photon processes under the intrinsic decoherence. The nonlinear unitary interactions lead to generating different types of nonlocal correlations via Bell nonlocality, trace-norm measurement-induced non-locality (MIN), and Bures-distance entanglement. Based on the intrinsic decoherence, the two-qubit states have stationary amounts of the MIN-correlation and Bures distance entanglement with more stability. It is found that the qubit–qubit interaction coupling is affected as additional decoherence. It leads to more oscillations and stability. The enhancement of the amount of the generated nonlocal correlations depends on the superposition of Barut-Girardello coherent states. The phenomenon of sudden birth/death and the Bell non-locality can be enhanced when the two-mode parametric amplifier cavity is initially prepared in the coherent states.
The dynamics of two charged qubits containing Josephson Junctions inside a cavity are investigated under the intrinsic decoherence effect. New types of quantum correlations via local quantum Fisher information and Bures distance norm are explored. We show that we can control the quantum correlations robustness by the intrinsic decoherence rate, the qubit-qubit coupling as well as by the initial coherent states superposition. The phenomenon of sudden changes and the freezing behavior for the local quantum Fisher information are sensitive to the initial coherent state superposition and the intrinsic decoherence.
In a system of two charge-qubits that are initially prepared in a maximally entangled Bell's state, the dynamics of quantum memory-assisted entropic uncertainty, purity, and negative entanglement are investigated. Isolated external cavity fields are considered in two different configurations: coherent-even coherent and even coherent cavity fields. For different initial cavity configurations, the temporal evolution of the final state of qubits and cavities is solved analytically. The effects of intrinsic decoherence and detuning strength on the dynamics of bipartite entropic uncertainty, purity and entanglement are explored. Depending on the field parameters, nonclassical correlations can be preserved. Nonclassical correlations and revival aspects appear to be significantly inhibited when intrinsic decoherence increases. Nonclassical correlations stay longer and have greater revivals due to the high detuning of the two qubits and the coherence strength of the initial cavity fields. Quantum memory-assisted entropic uncertainty and entropy have similar dynamics while the negativity presents fewer revivals in contrast.
The generated nonlocal correlations of two superconducting-charge (SCC) qubits including uncertainty-induced nonlocality (UIN), Bell-Horodecki nonlocality, and negativity’s entanglement have been explored by intrinsic decoherence model. An initial separable two SCC-qubits state to study the generation of nonlocal correlations. By adjusting the intrinsic decoherence intensity and the two superconducting-qubits interaction parameters (of Josephson energies, the mutual two SCC-qubits coupling energy, and the difference between the Josephson SCC-qubit energies), we can control the produced maximum Bell-Horodecki nonlocality, UIN, and entanglement, which their dynamics align with the hierarchy principle. It is found that the generations of two-qubit states, having Bell-Horodecki nonlocality, UIN, and negativity entanglement, by the interactions of two SCC-qubits depend on their interaction parameters and intrinsic decoherence. For weak mutual two SCC-qubits coupling energy and the Josephson SCC-qubit energies with a slight difference between the Josephson SCC-qubit energies, the generated two SCC-qubit state has strong nonlocal correlation dynamics. The mutual coupling energy for two SCC-qubits can enhance the generation of weak nonlocal correlation dynamics when there is a significant difference between the Josephson SCC-qubit energies. Controlling Josephson energy, mutual coupling, and the energy difference of SCC-qubits can improve nonlocal correlations’ robustness against intrinsic decoherence.
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.