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

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Watts, Paul, O'Connor, Maurice and Vala, Jiri (2013) Metric Structure of the Space of Two-Qubit Gates, Perfect Entanglers and Quantum Control. Entropy, 15. pp. 1963-1984. ISSN 1099-4300

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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.

Item Type:	Article
Additional Information:	The definitive version of this article is available at doi:10.3390/e15061963 . © 2013 by the authors; licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution license (http://creativecommons.org/licenses/by/3.0/).
Keywords:	two-qubit systems; metric spaces; Haar measure;
Academic Unit:	Faculty of Science and Engineering > Mathematical Physics
Item ID:	4503
Depositing User:	Dr. Jiri Vala
Date Deposited:	18 Sep 2013 15:52
Journal or Publication Title:	Entropy
Publisher:	MDPI
Refereed:	Yes
Related URLs:	http://www.mdpi.com/journal/entropy
Use Licence:	This item is available under a Creative Commons Attribution Non Commercial Share Alike Licence (CC BY-NC-SA). Details of this licence are available here

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