Next Article in Journal
Inequality of Chances as a Symmetry Phase Transition
Next Article in Special Issue
Quantum Thermodynamics: A Dynamical Viewpoint
Previous Article in Journal
Deepening the Conception of Functional Information in the Description of Zoonotic Infectious Diseases
Previous Article in Special Issue
Genuine Tripartite Entanglement and Nonlocality in Bose-Einstein Condensates by Collective Atomic Recoil
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

1,2
,
1
 and
1,2,*
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)
Download PDF [1013 KB, 24 February 2015; original version 24 February 2015]

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 which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Share & Cite This Article

Further Mendeley | CiteULike
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.

View more citation formats

Related Articles

Article Metrics

For more information on the journal, click here

Comments

Cited By

[Return to top]
Entropy EISSN 1099-4300 Published by MDPI AG, Basel, Switzerland RSS E-Mail Table of Contents Alert