Abstract
In recent years, an approach to discrete quantum phase spaces which comprehends all the main quasiprobability distributions known has been developed. It is the research that started with the pioneering work of Galetti and Piza, where the idea of operator bases constructed of discrete Fourier transforms of unitary displacement operators was first introduced. Subsequently, the discrete coherent states were introduced, and finally, the s-parametrized distributions, that include the Wigner, Husimi, and Glauber–Sudarshan distribution functions as particular cases. In the present work, we adapt its formulation to encompass some additional discrete symmetries, achieving an elegant yet physically sound formalism.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
D. Galetti and A. F. R. de Toledo Piza, Physica A, 149 267 (1988).
W. K. Wooters, Ann. Phys. (NY), 176, 1 (1987).
O. Cohendet O, P. Combe, M. Sirugue, and M. Sirugue-Collin, J. Phys. A: Math. Gen., 21, 2875 (1988).
M. Ruzzi, M. A. Marchiolli, and D. Galetti, J. Phys. A: Math. Gen., 38, 6239 (2005).
T. Opatný, D.-G. Welsch, and V. Bužek, Phys. Rev. A, 53, 3822 (1996).
K. E. Cahill and R. J. Glauber, Phys. Rev., 177, 1857 (1969).
K. E. Cahill and R. J. Glauber, Phys. Rev., 177, 1882 (1969).
A. B. Klimov, C. Muñoz, and L. L. Sánchez-Soto, Phys. Rev. A, 80, 043836 (2009).
D. Galetti and M. A. Marchiolli, Ann. Phys. (NY), 249, 454 (1996).
M. Ruzzi, J. Math. Phys., 47, 063507 (2006).
M. A. Marchiolli and M. Ruzzi, “First considerations on the generalized uncertainty principle for finite-dimensional discrete phase spaces,” arXiv: quant-ph/1106.2500.
M. Ruzzi, J. Phys. A: Math. Gen., 35, 1763 (2002).
M. Ruzzi and D. Galetti, J. Phys. A: Math. Gen., 35, 4633 (2002).
M. Ruzzi, S. S. L. Machado, and D. Galetti, Braz. J. Phys., 33, 259 (2003).
L. Barker, J. Funct. Anal., 186, 153 (2001).
L. Barker, J. Phys A: Math. Gen., 22, 4673 (2001).
L. Barker, J. Math. Phys., 42, 4653 (2001).
N. Ja. Vilenkin and A. V. Klimyk, Representation of Lie Groups and Special Functions: Simplest Lie Groups, Special Functions and Integral Transforms, Kluwer Academic Publishers, Dordrecht (1992).
R. Bellman, A Brief Introduction to Theta Functions, Holt, Rinehart and Winston, New York (1961).
W. Magnus, F. Oberhettinger, and R. P. Soni, Formulas and Theorems for the Special Functions of Mathematical Physics, Springer, New York (1966).
E. T. Whittaker and G. N.Watson, A Course of Modern Analysis, Cambridge Mathematical Library, Cambridge University Press (2000).
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Marchiolli, M.A., Ruzzi, M. Quasidistributions and coherent states for finite-dimensional quantum systems. J Russ Laser Res 32, 381–392 (2011). https://doi.org/10.1007/s10946-011-9226-y
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10946-011-9226-y