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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

Department of Mathematical Physics, National University of Ireland Maynooth, Science Building, North Campus, Maynooth, Co. Kildare, Ireland
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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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. View Full-Text
Keywords: two-qubit systems; metric spaces; Haar measure two-qubit systems; metric spaces; Haar measure

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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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