In U(1)-symmetric random circuits, initial states with lower stabilizer Rényi entropy generate nonstabilizerness faster than those with higher entropy, with the effect also depending on spatial charge structure and extending to SU(2) circuits and Hamiltonian dynamics.
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Two quantum states ρ₁ and ρ₂ commute exactly when tr(ρ₁²ρ₂²) = tr(ρ₁ ρ₂ ρ₁ ρ₂).
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Nonstabilizerness Mpemba Effects
In U(1)-symmetric random circuits, initial states with lower stabilizer Rényi entropy generate nonstabilizerness faster than those with higher entropy, with the effect also depending on spatial charge structure and extending to SU(2) circuits and Hamiltonian dynamics.
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Commutativity from a single Bargmann invariant equality
Two quantum states ρ₁ and ρ₂ commute exactly when tr(ρ₁²ρ₂²) = tr(ρ₁ ρ₂ ρ₁ ρ₂).