Some remarks on the wigner distribution

Piotr Kazimierczyk, Arkadiusz Orłowski

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.

GERALD J. IAFRATE, H. L. Grubin, David K. Ferry

Ryo Harada

Husimi distributions [11] and Wigner distributions [20] are well-known quasi-probability distributions which appear in several contexts. In this paper, we show some remarkable aspects of these distribution functions related to geometric structures of generalized coherent state systems [15,16] and operational quantum physics [7], and a scheme of formulating generalized version of quasi-probability distributions. Our scheme gives concrete formulae of quasi-probability distributions in more direct way from the theory of coherent state systems and clarify their operational meanings, especially of Husimi distributions and mutual relation between Husimi distributions and other classes of quasi-probability distributions.