Doped matchgate circuits achieve approximate parity-preserving 2-designs in polylogarithmic depth using a sparse number of non-Gaussian gates, with the design formation mapped exactly to a birth-death Markov chain.
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In charge- and dipole-conserving fragmented systems, charge and dipole asymmetries exhibit Mpemba-like crossings on parametrically distinct timescales, driven by frozen sectors retaining asymmetry and active sectors relaxing.
A new Gaussian asymmetry measure is defined that quantifies the minimal distance from a Gaussian state to the manifold of symmetric Gaussian states while capturing established dynamical signatures of entanglement asymmetry.
Introduces occupation number entropies (Tsallis) and natural-orbital participation entropies (Renyi) as computable convex resource monotones for fermionic non-Gaussianity from the covariance matrix.
Haar random qubit states show vanishing fermionic non-Gaussianity for subsystems smaller than half the total size without symmetry, small but finite non-Gaussianity with U(1) symmetry, and extensive non-Gaussianity for larger subsystems.
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A Gaussian asymmetry measure
A new Gaussian asymmetry measure is defined that quantifies the minimal distance from a Gaussian state to the manifold of symmetric Gaussian states while capturing established dynamical signatures of entanglement asymmetry.