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arXiv:1111.4935

Information Entropy of Two Cooper Pair Boxes Interacting with an Environment

Heba Kadry Abdel-Hafez, Nordin Zakaria

Published Nov 21, 2011• 0 citations
arXivHTMLPDF

Abstract

Adopting the framework of two-coupled superconducting charges model, we discussed the information entropy of two qubits initially prepared in a mixed state and allowed to interact with their environment. The impact of the different parameters of the system is explicitly investigated. Present calculations show that strong mutual entropy is obtained for a long interaction time when the two qubits are initially in a mixed state with the environment switched off. We have identified a class of two-qubit states that have a rich dynamics when the deviation between the characteristic energies of the quabits becomes minimum. It was found that the total correlation decreases abruptly to zero in a finite time due to the influence of the strong environment.

DOI
10.48550/arxiv.1111.4935

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Adopting the framework of two-coupled superconducting charges model, we discussed the information entropy of two qubits initially prepared in a mixed state and allowed to interact with their environment. The impact of the different parameters of the system is explicitly investigated. Present calculations show that strong mutual entropy is obtained for a long interaction time when the two qubits are initially in a mixed state with the environment switched off. We have identified a class of two-qubit states that have a rich dynamics when the deviation between the characteristic energies of the quabits becomes minimum. It was found that the total correlation decreases abruptly to zero in a finite time due to the influence of the strong environment.
The dynamics of entanglement of two superconducting charge qubit system interacting with a squeezed coherent state were examined by means of linear entropy. The influence of the relative phase of the two qubits' levels and squeezing parameter on the time evolution of linear entropy was discussed. The results showed that the linear entropy almost tends to zero at half the revival time when the two qubits were initially in the maximally entangled state. It was also showed that a greater number of oscillations of the linear entropy were observed with the increasing of squeezing parameter and the sustainment time of the maximum entropy was increased. There was no change in the maximum value of the linear entropy. Moreover,the relative phase of the two qubits' levels decreased the degree of entanglement between the two qubits and the field.
The dynamics of a charged two-qubit system prepared initially in a maximum entangled state is discussed, where each qubit interacts independently with a dephasing channel. The Fisher information is used to estimate the channel and the energy parameters. Moreover, the contribution from different parts of Fisher information is discussed. We show that, the degree of estimation of any parameter depends on the initial value of this parameter. It turns out that the upper bounds of Fisher information with respect to the dephasing parameter increase and that corresponding to coupling parameter decreases as the initial energy of each qubit increases.
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.
We consider a single-Cooper-pair box biased by a classical voltage and also irradiated by a single-mode quantized field. We assume that the box is initially in a mixed state, and investigate the quantum dynamics of the Cooper-pair box and show that the collapse and revival phenomenon can exist in this system. We also study the quantum entropy of the single-Cooper-pair box and discuss the effects of the different parameters on this quantum entropy. We find that the box, which is initially in a mixed state, may evolve into an almost pure state.
The influence of the initial preparation on dephasing in open quantum dynamics is studied using an exactly solvable model of a two-level system (qubit) interacting with a bosonic bath. It is found that, for some classes of nonselective preparation measurements, qubit-bath correlations lead to a significant enhancement of coherence in the qubit at the initial stage of evolution. The time behavior of the qubit purity and entropy in the regime of enhancement of coherence is considered for different temperatures and coupling strengths.
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.