When is the Wigner function of multidimensional systems nonnegative ...
...It is shown that, for systems with an arbitrary number of degrees of freedom, a necessary and sufficient condition for the Wigner function to be nonnegative is that the corresponding state wavefunction is the exponential of a quadratic form....
https://pubs.aip.org/aip/jmp/article/24/1/97/226088/When-is-the-Wigner-function-of-multidimensional
When is the Wigner function of multidimensional systems nonnegative?
...It is shown that, for systems with an arbitrary number of degrees of freedom, a necessary and sufficient condition for the Wigner function to be nonnegative is that the corresponding state......
https://www.researchgate.net/profile/Francisco-Soto-Eguibar/publication/288838456_When_is_the_Wigner_function_of_multidimensional_systems_nonnegative_When_is_the_Wigner_function_of_multi-dimensional_systems_nonnegative/links/56869ba308aebccc4e13b7a7/When-is-the-Wigner-function-of-multidimensional-systems-nonnegative-When-is-the-Wigner-function-of-multi-dimensional-systems-nonnegative.pdf
?Francisco Soto-Eguibar? - ?Google Scholar?
...When is the Wigner function of multidimensional systems nonnegative? H Moya-Cessa, F Soto-Eguibar, JM Vargas-Martínez, R Juárez-Amaro, ... Differential equations. An operational approach.......
https://scholar.google.com/citations?user=s3YgS-kAAAAJ&hl=en
arXiv:quant-ph/0702004v1 31 Jan 2007
...d Wigner functions are non-negative. The authors aim to establish necessary require-men s for quantum computational speedup. Indeed, if the Wigner function of a quantum computer is positive at all times, then it operates only with stabilizer states and hence offers no advantage over classical computers, by the...
https://arxiv.org/pdf/quant-ph/0702004
When is the Wigner function of multidimensional sys... | PDF or Rental
...Summary: Abstract: It is shown that, for systems with an arbitrary number of degrees of freedom, a necessary and sufficient condition for the Wigner function to be nonnegative is that the corresponding state wavefunction is the exponential of a quadratic form....
https://articles.researchsolutions.com/when-is-the-wigner-function-of-multidimensional-systems-nonnegative/doi/10.1063/1.525607
Crossref Metadata Search
...On the probability density interpretation of smoothed Wigner functions JOURNAL ARTICLE published 7 October 1990 in Journal of Physics A: Mathematical and General...
https://search.crossref.org/search/works?from_ui=yes&q=R.%20L.%20Hudson:%20When%20is%20the%20Wigner%20quasi-probability%20density%20nonnegative?%20Rep.%20Math.%20Phys.%206%20(1974),%20249-252.
d. gross Non-negative Wigner functions in prime dimensions
...Further, we show how to lift the ambiguity in the ax-iomatic characterization of Wigner functions by requiring Clifford covariance, note that a unitary operator preserves positivity if and only it is a Clifford operation, discuss the relation of various ways to introduce Wigner functions and stabilizer states in dimensions of the form d pn ......
https://link.springer.com/content/pdf/10.1007/s00340-006-2510-9.pdf
How is Hudson's theorem for the Wigner function proved?
...Hudson's theorem tells us that a pure state has non-negative Wigner function iff it's Gaussian. This was originally proven in [Hudson 1974], and then generalised to multidimensional systems in [Soto and Claverie 1983]....
https://physics.stackexchange.com/questions/813023/how-is-hudsons-theorem-for-the-wigner-function-proved
Wigner quasiprobability distribution - Wikipedia
...This Wigner transformation (or map) is the inverse of the Weyl transform, which maps phase-space functions to Hilbert-space operators, in Weyl quantization. Thus, the Wigner function is the cornerstone of quantum mechanics in phase space....
https://en.wikipedia.org/wiki/Wigner_quasiprobability_distribution
Nonnegative mixed states in Weyl?Wigner?Moyal theory
...A theorem of Hudson [1], generalized to the -dimensional case by Soto and Claverie [2], establishes that the only nonnegative distribution functions corresponding to pure states in the Weyl?Wigner?Moyal (WWM) formulation of Quantum Mechanics are the Wigner transforms of gaussian wavefunctions....
https://www.kerwa.ucr.ac.cr/bitstreams/3aa573b8-6a0e-4a65-85d6-ac3fc11e8aaa/download