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

1,2email, 1email and 1,2,* email
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)
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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
PDF Full-text Download PDF Full-Text [1013 KB, Updated Version, uploaded 27 May 2013 13:39 CEST]
The original version is still available [1013 KB, uploaded 23 May 2013 13:38 CEST]

Export to BibTeX |
EndNote


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.

Entropy EISSN 1099-4300 Published by MDPI AG, Basel, Switzerland RSS E-Mail Table of Contents Alert