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Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE

Four-qubit cluster state entanglement in the presence of decoherence

Gerald N. Gilbert, Yaakov S. Weinstein

Published Apr 13, 2010• 0 citations
Publisher

Abstract

The highly entangled four qubit cluster state can be used to perform an arbitrary single logical qubit rotation via the techniques of measurement-based quantum computation. In this paper, we explore the relationship between the entanglement in the cluster state and the ability of the state to accurately perform the desired logical rotation. This has important experimental ramifications as realistic cluster state experiments will always be subject to decoherence. We also note the exhibition of entanglement sudden death (ESD) and ask how severely its onset affects the utilization of the cluster state as a means of implementing the arbitrary single logical qubit rotation.

DOI
10.1117/12.850328

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•Jan 1, 2015•1 citation
The highly entangled four qubit cluster state can be used to perform an arbitrary single logical qubit rotation via the techniques of measurement-based quantum computation. In this paper, we explore the relationship between the entanglement in the cluster state and the ability of the state to accurately perform the desired logical rotation. This has important experimental ramifications as realistic cluster state experiments will always be subject to decoherence. We also note the exhibition of entanglement sudden death (ESD) and ask how severely its onset affects the utilization of the cluster state as a means of implementing the arbitrary single logical qubit rotation.
In this paper we utilize superoperator formalism to explore the entanglement evolution of four-qubit cluster states in a number of decohering environments. A four-qubit cluster state is a resource for the performance of an arbitrary single-logical-qubit rotation via measurement-based cluster-state quantum computation. We are specifically interested in the relationship between entanglement evolution and the fidelity with which the arbitrary single-logical-qubit rotation can be implemented in the presence of decoherence as this will have important experimental ramifications. We also note the exhibition of entanglement sudden death (ESD) and ask how severely its onset affects the utilization of the cluster state as a means of implementing an arbitrary single-logical-qubit rotation.
I explore the entanglement evolution of a four-qubit cluster state in a dephasing environment concentrating on the phenomenon of entanglement sudden death (ESD). Specifically, I ask whether the onset of ESD has an effect on the utilization of this cluster state as a means of implementing a single-qubit rotation in the measurement-based cluster state model of quantum computation. To do this, I compare the evolution of the entanglement to the fidelity, a measure of how accurately the desired state (after the measurement-based operations) is achieved. I find that ESD does not cause a change in behavior or discontinuity in the fidelity but may indicate for certain states when the fidelity goes to 0.5.
When two entangled qubits, each owned by Alice and Bob, undergo separate decoherence, the amount of entanglement is reduced, and often, weak decoherence causes complete loss of entanglement, known as entanglement sudden death. Here we show that it is possible to apply quantum measurement reversal on a single-qubit to avoid entanglement sudden death, rather than on both qubits. Our scheme has important applications in quantum information processing protocols based on distributed or stored entangled qubits as they are subject to decoherence.
High fidelity, high count rate four qubit linear cluster states have been realized by using two photons that are entangled both in polarization and linear momentum. Their properties have been investigated by evaluating the entanglement witness and carrying out a "stronger two observer all versus nothing" test of quantum nonlocality. The experimental results concerning the realization of single qubit rotations demonstrates the feasibility of one-way quantum computation by using these states.