Wigner function for a particle in an infinite lattice

Abstract

We study the Wigner function for a quantum system with a discrete, infinite dimensional Hilbert space, such as a spinless particle moving on a one dimensional infinite lattice. We discuss the peculiarities of this scenario and of the associated phase space construction, propose a meaningful definition of the Wigner function in this case, and characterize the set of pure states for which it is non-negative. We propose a measure of non-classicality for states in this system which is consistent with the continuum limit. The prescriptions introduced here are illustrated by applying them to localized and Gaussian states, and to their superpositions.

19 pages (single column), 7 figures

References in corpus (4)

• Classicality in discrete Wigner functions
• Discrete Wigner functions and quantum computational speedup
• Directly estimating non-classicality
• Non-negative Wigner functions in prime dimensions

Cited by in corpus (6)

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• Normalizer Circuits and Quantum Computation
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• Bath-induced correlations in an infinite-dimensional Hilbert space
• Twisted Fourier analysis and pseudo-probability distributions