Quantum

Stabilizer R\'enyi Entropy Without a Phase Reference

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Briefings

A new invariant, phase-averaged stabilizer R\'enyi entropy, quantifies magic relative to unspecified Pauli axes in quantum systems. It is exactly invariant under independent local rephasings and vanishes for pure stabilizer states. For sparse supports, it yields a closed-form function of basis-state probabilities. The ceiling for $n$ channels is $rac{7}{5}$ for two channels and $rac{3}{6-5}$ for $n ext{ channels} ext{ (approx } rac{27}{13} ext{ for } 3 o 2 ext{ scattering)}. It applies to tree-level gluon scattering at four and five points, saturating two- and three-channel ceilings. The invariant is independent of fixed external colors.

Key points

• The phase-averaged stabilizer R\'enyi entropy is exactly invariant under independent local rephasings, making it suitable for systems where computational basis axes are unspecified.
• For sparse supports, the entropy reduces to a closed-form function of basis-state probabilities, with a ceiling of $rac{7}{5}$ for two channels and $rac{27}{13}$ for three-channel scattering.

Context and limitations

The analysis covers tree-level gluon scattering at four and five points. Results for general $n$ channels are theoretical ceilings. The invariant is independent of fixed external colors but does not specify the external color values themselves.

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