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

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.

27 pages, 5 figures

References in corpus (2)

• Unitary quantum gates, perfect entanglers and unistochastic maps
• Composite parameterization and Haar measure for all unitary and special unitary groups

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