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Optica Applicata

Time-dependent Pancharatnam phases and quantum correlations for coupling superconducting two-qubit system with dissipative environment

Liyuan Xue, Z.S. Wang

Published Jan 1, 2020• 0 citations
Publisher

Abstract

Two coupling superconducting qubits are studied for the quantum concurrence, discord, and Pancharatnam phase, for the X and Y states under the dephasing and instantaneous decay environment as well as their couplings. We find that the X and Y states are special mixed states according to the Bloch radius. In general, the larger the environment and phonon number are at the larger region of time, the larger the quantum concurrence and discord are. But we find that the environment correlations are helpful to implement the quantum computation. The Pancharatnam phases provide a way to distinguish the X and Y states.

DOI
10.37190/oa200402

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Two coupling superconducting qubits are studied for the quantum concurrence, discord, and Pancharatnam phase, for the X and Y states under the dephasing and instantaneous decay environment as well as their couplings. We find that the X and Y states are special mixed states according to the Bloch radius. In general, the larger the environment and phonon number are at the larger region of time, the larger the quantum concurrence and discord are. But we find that the environment correlations are helpful to implement the quantum computation. The Pancharatnam phases provide a way to distinguish the X and Y states.
We investigated the geometric phase for interaction between superconducting two-qubit system in dephased environment. The Pancharatnam phase and the Berry phase are studied. Numerical results are discussed. By considering the differently initial conditions, we find that the time-dependent Pancharatnam phase keeps the initial entangling message. On the other hand, the transition of Pancharatnam phase is dependent of the phase change in the superconducting two-qubit coupling system. Our results may be helpful to implement the time-dependent geometric quantum computation.
In this work, we study quantum correlations in mixed states. The states studied are modeled by a two-qubit system interacting with its environment via a quantum non demolition (purely dephasing) as well as dissipative type of interaction. The entanglement dynamics of this two qubit system is analyzed. We make a comparative study of various measures of quantum correlations, like Concurrence, Bell's inequality, Discord and Teleportation fidelity, on these states, generated by the above evolutions. We classify these evoluted states on basis of various dynamical parameters like bath squeezing parameter rrr, inter-qubit spacing r12r_{12}r12​, temperature TTT and time of system-bath evolution ttt. In this study, in addition we report the existence of entangled states which do not violate Bell's inequality, but can still be useful as a potential resource for teleportation. Moreover we study the dynamics of quantum as well as classical correlation in presence of dissipative coherence.
The time evolution of a single Cooper pair in the presence of another Cooper pair interacting with an electromagnetic field in a dissipative cavity is presented. The strong dependence of the dynamics of two superconducting charge qubits interacting with the microcavity field on the instantaneous phase shift experienced by the second qubit is demonstrated. The Pancharatnam phase is found to be more sensitive than the population dynamics to the phase shift. This leads us to suggest a new technique for controlling the system dynamics. Furthermore, although the atom is not directly coupled to the cavity modes, its coherent properties are found to be strongly influenced by dissipation, both qualitatively and quantitatively.
In this work, we study quantum correlations in mixed states. The states studied are modeled by a two-qubit system interacting with its environment via a quantum non demolition (purely dephasing) as well as dissipative type of interaction. The entanglement dynamics of this two qubit system is analyzed. We make a comparative study of various measures of quantum correlations, like Concurrence, Bell's inequality, Discord and Teleportation fidelity, on these states, generated by the above evolutions. We classify these evoluted states on basis of various dynamical parameters like bath squeezing parameter rrr, inter-qubit spacing r12r_{12}r12​, temperature TTT and time of system-bath evolution ttt. In this study, in addition we report the existence of entangled states which do not violate Bell's inequality, but can still be useful as a potential resource for teleportation. Moreover we study the dynamics of quantum as well as classical correlation in presence of dissipative coherence.
In this paper, we have investigated the dynamics of the quantum correlation between two qubits of a system composed of an arbitrary number of qubits dissipating into a common environment. Our results imply that, when the initial state of the system contains one excitation, the quantum correlation of the quantum discord and the entanglement of formation can be generated between two qubits which have no interaction with each other but are interacting with a common environment. From our analysis, we find that the dynamics of the quantum discord and the entanglement of formation depends not only on the scaled time but also on the size of the system. The larger the size of the system is, the less the quantum discord and the entanglement of formation is generated. By using a comparison between the quantum discord and the entanglement of formation, we find that the quantum discord is more robust to the size of the system than the entanglement of formation is, in the sense that the former decreases more slowly with an increase of the size of the system than the latter does. In addition, the case of the initial state with two excitations is discussed.
The decay of correlations between two qubits under the influence of a squeezed thermal reservoir is investigated by means of the quantum master equation in the Born–Markov approximation. To find the effect of the reservoir squeezing on the two-qubit correlations, concurrence, quantum discord, classical correlation and total correlation are calculated for the X-states. It is found that, except for quantum discord, the reservoir squeezing always suppresses the decay of the correlations during the time evolution. On the other hand, for quantum discord, the reservoir squeezing enhances the decay in the initial and intermediate time regions while it reduces the decay in the long time region.