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International Journal of Quantum Information

ENTANGLEMENT OF TWO COUPLED CHARGE QUBITS

Yu. A. Pashkin, Todd Tilma, D. V. Averin, O. V. Astafiev, Tsuyoshi Yamamoto, Yasunobu Nakamura, Franco Nori, Jaw-Shen Tsai

Published Dec 1, 2003• 9 citations
Publisher

Abstract

We have analyzed the entanglement of a system of two coupled charge qubits. We calculate the amount of entanglement using several different approaches. We show that in the ideal case the system remains entangled most of the time and the amount of entanglement reaches almost unity, i.e. the system becomes maximally entangled at certain instances.

DOI
10.1142/s0219749903000334

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We have analyzed and measured the quantum coherent dynamics of a circuit containing two coupled superconducting charge qubits. Each qubit is based on a Cooper pair box connected to a reservoir electrode through a Josephson junction. Two qubits are coupled electrostatically by a small island overlapping both Cooper pair boxes. Quantum state manipulation ofthe qubit circuit is done by applying non-adiabatic voltage pulses to the common gate. We read out each qubit by means of probe electrodes connected to Cooper pair boxes through high-Ohmic tunnel junctions. With such a setup the measured pulse-induced probe currents are proportional to the probability for each qubit to have an extra Cooper pai1r after the manipulation. As expected from theory and observed experimentally the measured pulse-induced current in each probe has two frequency components whose position on the frequency axis can be externally controlled. This is a result ofthe inter-qubit coupling which is also responsible for the avoided level crossing that we observed in the qubits' spectra. Our simulations show that in the absence of decoherence and with a rectangular pulse shape the system remains entangled most ofthe time reaching maximally entangled states at certain instances.
In this paper, we study the entanglement in a five qubit model. For this purpose, we consider two non-interacting systems A and B which are correlated together initially. A is a t wo atoms Tavis-Cu mmings system and B is a Jaynes-Cummings System. By choosing a convenient initial condition which shows the initially correlation, our total system (A plus B) become a system which consist of five qubits. There are ten pairwise concurrences which we must calculate. We show that initially non-entangled qubits become entangled by passing time, the process which may be interpreted as entanglement transfer. We also show that our model in special cases become two-qubit and three-qubit models and analyze entanglement in these special cases.