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

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; in revised form: 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

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MDPI and ACS Style

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.

AMA Style

Watts P, O'Connor M, Vala J. Metric Structure of the Space of Two-Qubit Gates, Perfect Entanglers and Quantum Control. Entropy. 2013; 15(6):1963-1984.

Chicago/Turabian Style

Watts, Paul; O'Connor, Maurice; Vala, Jiří. 2013. "Metric Structure of the Space of Two-Qubit Gates, Perfect Entanglers and Quantum Control." Entropy 15, no. 6: 1963-1984.

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