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Entropy 2013, 15(6), 1963-1984; doi:10.3390/e15061963

Metric Structure of the Space of Two-Qubit Gates, Perfect Entanglers and Quantum Control

1
Department of Mathematical Physics, National University of Ireland Maynooth, Science Building, North Campus, Maynooth, Co. Kildare, Ireland
2
School of Theoretical Physics, Dublin Institute for Advanced Studies, 10 Burlington Road,Dublin 4, Ireland
*
Author to whom correspondence should be addressed.
Received: 7 April 2013 / Revised: 17 April 2013 / Accepted: 17 May 2013 / Published: 23 May 2013
(This article belongs to the Special Issue Quantum Information 2012)
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Abstract

We derive expressions for the invariant length element and measure for the simple compact Lie group SU(4) in a coordinate system particularly suitable for treating entanglement in quantum information processing. Using this metric, we compute the invariant volume of the space of two-qubit perfect entanglers. We find that this volume corresponds to more than 84% of the total invariant volume of the space of two-qubit gates. This same metric is also used to determine the effective target sizes that selected gates will present in any quantum-control procedure designed to implement them.
Keywords: two-qubit systems; metric spaces; Haar measure two-qubit systems; metric spaces; Haar measure
This is an open access article distributed under the Creative Commons Attribution License (CC BY 3.0).

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Watts, P.; O'Connor, M.; Vala, J. Metric Structure of the Space of Two-Qubit Gates, Perfect Entanglers and Quantum Control. Entropy 2013, 15, 1963-1984.

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