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Title: Non-negative Wigner functions for orbital angular momentum states

Abstract

The Wigner function of a pure continuous-variable quantum state is non-negative if and only if the state is Gaussian. Here we show that for the canonical pair angle and angular momentum, the only pure states with non-negative Wigner functions are the eigenstates of the angular momentum. Some implications of this surprising result are discussed.

Authors:
;  [1];  [2]; ;  [3]
  1. Departamento de Optica, Facultad de Fisica, Universidad Complutense, E-28040 Madrid (Spain)
  2. Departamento de Fisica, Universidad de Guadalajara, 44420 Guadalajara, Jalisco (Mexico)
  3. Department of Optics, Palacky University, 17. listopadu 50, CZ-772 00 Olomouc (Czech Republic)
Publication Date:
OSTI Identifier:
21408142
Resource Type:
Journal Article
Journal Name:
Physical Review. A
Additional Journal Information:
Journal Volume: 81; Journal Issue: 1; Other Information: DOI: 10.1103/PhysRevA.81.012101; (c) 2010 The American Physical Society; Journal ID: ISSN 1050-2947
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; EIGENSTATES; FUNCTIONS; ORBITAL ANGULAR MOMENTUM; WIGNER DISTRIBUTION; ANGULAR MOMENTUM

Citation Formats

Rigas, I, Sanchez-Soto, L L, Klimov, A B, Rehacek, J, and Hradil, Z. Non-negative Wigner functions for orbital angular momentum states. United States: N. p., 2010. Web. doi:10.1103/PHYSREVA.81.012101.
Rigas, I, Sanchez-Soto, L L, Klimov, A B, Rehacek, J, & Hradil, Z. Non-negative Wigner functions for orbital angular momentum states. United States. https://doi.org/10.1103/PHYSREVA.81.012101
Rigas, I, Sanchez-Soto, L L, Klimov, A B, Rehacek, J, and Hradil, Z. 2010. "Non-negative Wigner functions for orbital angular momentum states". United States. https://doi.org/10.1103/PHYSREVA.81.012101.
@article{osti_21408142,
title = {Non-negative Wigner functions for orbital angular momentum states},
author = {Rigas, I and Sanchez-Soto, L L and Klimov, A B and Rehacek, J and Hradil, Z},
abstractNote = {The Wigner function of a pure continuous-variable quantum state is non-negative if and only if the state is Gaussian. Here we show that for the canonical pair angle and angular momentum, the only pure states with non-negative Wigner functions are the eigenstates of the angular momentum. Some implications of this surprising result are discussed.},
doi = {10.1103/PHYSREVA.81.012101},
url = {https://www.osti.gov/biblio/21408142}, journal = {Physical Review. A},
issn = {1050-2947},
number = 1,
volume = 81,
place = {United States},
year = {Fri Jan 15 00:00:00 EST 2010},
month = {Fri Jan 15 00:00:00 EST 2010}
}