Defines bridge degree monotone for fermionic non-Gaussianity from Bell-sampling eigenvalues of Lambda, shows non-increase under Gaussian protocols for stronger no-go theorems, and gives polynomial-sample tests for Gaussianity and 2-designs.
Reardon-Smith, The fermionic linear optical extent is multiplicative for 4 qubit parity eigenstates, arxiv:2407.20934 (2024)
4 Pith papers cite this work. Polarity classification is still indexing.
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Introduces practical witnesses of fermionic non-Gaussianity via antiflatness from covariance matrices, with two efficient measurement protocols, a purity-corrected version for mixed states, and experimental results on an IQM processor showing noise effects and requirements for pseudorandom states.
Block-product paired non-Gaussian fermionic states allow efficient classical additive-error approximation of transition amplitudes, overlaps, and high-weight correlators under free-fermionic dynamics using multivariate Pfaffian polynomials.
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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Non-Gaussianity of random quantum states
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.