Remarks on a classification of Wigner distributions

Felix Alexandrovich Berezin

Joachim J. Włodarz

Giuseppe Gaeta

It was recently remarked by Lutz [Phys. Rev. A 67, 051402(R) (2003)] that the equation for the marginal Wigner distribution in an optical lattice admits a scale-free distribution corresponding to Tsallis statistics. Here we show that this distribution is invariant under an asymptotic symmetry of the equation and hence that this scale-free behavior can be understood in terms of symmetry analysis.

Vitaly V. Kocharovsky, Kunwar Kalra

The computational complexity, or quantum advantage, of Gaussian boson sampling is ascribed to squeezing of the Wigner quasiprobability distribution. This approach reveals the physical origin of the quantum complexity resource. This approach sets an easy-to-compute universal lower bound for the complexity dimension determined by the boson number in the quantum complexity resource. It is shown that the Wigner lower bound is close to the exact value of the complexity dimension obtained via numerical convex optimization. Our analytical and numerical results disclose a series of remarkable properties of quantum advantage.

R. Simon, E. C. G. Sudarshan, Narasimhaiengar Mukunda

M. Revzen