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arXiv:1210.6971 · Communications in Theoretical Physics

Skew Information for a Single Cooper Pair Box Interacting with a Single Cavity Field

NASSER METWALLY, A Mannai, Mahmoud Abdel‐Aty

Published Jun 1, 2013• 8 citations
arXivHTMLPDF

Abstract

The dynamics of the skew information (SI) is investigated for a single Cooper Pair Box (CPB) interacting with a single cavity field. By suitably choosing the system parameters and precisely controlling the dynamics, novel connection is found between the SI and entanglement generation. It is shown that SI can be increased and reach its maximum value either by increasing the number of photons inside the cavity or considering the far off-resonant case. The number of oscillations of SI is increased by decreasing this ratio between the Josephson junction capacity and the gate capacity. This leads to significant improvement of the travelling time between the maximum and minimum values.

DOI
10.1088/0253-6102/59/6/20

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The dynamics of the skew information (SI) is investigated for a single Cooper Pair Box (CPB) interacting with a single cavity field. By suitably choosing the system parameters and precisely controlling the dynamics, novel connection is found between the SI and entanglement generation. It is shown that SI can be increased and reach its maximum value either by increasing the number of photons inside the cavity or considering the far off-resonant case. The number of oscillations of SI is increased by decreasing this ratio between the Josephson junction capacity and the gate capacity. This leads to significant improvement of the travelling time between the maximum and minimum values.
We describe an assembly of N Cooper-pair boxes (CPB) contained in a single mode cavity. In the dispersive regime, the correlation between the cavity field and each Cooper-pair box results in an effective interaction between CPBs that can be used to dynamically generate maximally entangled states. With only collective manipulations, we show how to create maximally entangled quantum states and how to use these states to reach the Heisenberg limit in the determination of a spectroscopy frequency. This scheme can be applied to other types of superconducting qubits.
The original dense coding protocol is achieved via a quantum channel generated between a single Cooper pair and a cavity. The dynamics of the coded and decoded information is investigated for different values of the channel’s parameters. It is shown that these two types of information increase as the detuning parameter increases or the number of photons inside the cavity decreases. The coded and decoded information increases as the ratio of the capacities between the box and the gate decrease. The dynamics of information is investigated in the presence of imperfect operation during the coding process. It is found that, for the phase flip error, the upper bound of the coded and decoded information is much smaller than that depicted for the bit flip errors.
A Hamiltonian which represents the interaction between a single Cooper-pair box and two quantized electromagnetic fields is considered in order to find new ways for quantum information. The wave function in Schrdinger picture is obtained. The evolution of the entropy of the box as a function of the scaled time is ploted to measure the entanglement between the box and the fields. It is found that the entanglement is sensitive to the detuning between the Josephson energy and the fields frequency, increasing the detuning can decrease the entanglement.