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

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 ent...

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Bibliographic Details
Published in:Entropy (Basel, Switzerland) Switzerland), 2013-06, Vol.15 (6), p.1963-1984
Main Authors: Watts, Paul, O'Connor, Maurice, Vala, Jiří
Format: Article
Language:English
Subjects:
Haar measure
metric spaces
two-qubit systems
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Summary: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.
ISSN:1099-4300
1099-4300
DOI:10.3390/e15061963