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arxiv: 1306.2811 · v1 · submitted 2013-06-12 · 🪐 quant-ph

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

Paul Watts , Maurice O'Connor , Jiri Vala
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classification 🪐 quant-ph
keywords gatesinvariantmetricspacetwo-qubitvolumeentanglersperfect
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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.

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Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score.

  1. On the KAK Decomposition and Equivalence Classes

    quant-ph 2026-05 unverdicted novelty 6.0

    For SU(4), local equivalence classes under SU(2)⊗SU(2) multiplication are not geometrically represented by the Weyl chamber; that chamber appears only under projective-local equivalence that ignores global phases.