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Searching for highly entangled multi-qubit states

Brown, I.D.K., Stepney, S., Sudbery, A. and Braunstein, S.L. (2005) Searching for highly entangled multi-qubit states. Journal of Physics A: Mathematical and General, 38 (5). pp. 1119-1131. ISSN 03054470

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Abstract

We present a simple numerical optimization procedure to search for highly entangled states of 2, 3, 4 and 5 qubits. We develop a computationally tractable entanglement measure based on the negative partial transpose criterion, which can be applied to quantum systems of an arbitrary number of qubits. The search algorithm attempts to optimize this entanglement cost function to find the maximal entanglement in a quantum system. We present highly entangled 4-qubit and 5-qubit states discovered by this search. We show that the 4-qubit state is not quite as entangled, according to two separate measures, as the conjectured maximally entangled Higuchi–Sudbery state. Using this measure, these states are more highly entangled than the 4-qubit and 5-qubit GHZ states. We also present a conjecture about the NPT measure, inspired by some of our numerical results, that the single-qubit reduced states of maximally entangled states are all totally mixed.

Item Type: Article
Institution: The University of York
Academic Units: The University of York > Computer Science (York)
The University of York > Mathematics (York)
Depositing User: York RAE Import
Date Deposited: 20 Apr 2009 11:59
Last Modified: 20 Apr 2009 11:59
Published Version: http://dx.doi.org/10.1088/0305-4470/38/5/013
Status: Published
Publisher: Institute of Physics
Identification Number: 10.1088/0305-4470/38/5/013
URI: http://eprints.whiterose.ac.uk/id/eprint/6843

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