Abstract
The entropies associated with tomographic-probability distributions describing quantum and classical states are discussed. The inequalities for the tomographic entropies of quantum states are reviewed. Examples of both discrete variables (qudits, spins) and continuous variables (photon quadratures, positions and momenta) are studied.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
C. E. Shannon, Bell Syst. Tech. J., 27, 379 (1948).
A. Rényi, Probability Theory, North-Holland, Amsterdam (1970).
L. D. Landau, Z. Phys., 45, 430 (1927).
J. von Neumann, Mathematische Grundlagen der Quantummechanyk, Springer, Berlin (1932).
S. Mancini, V. I. Man’ko, and P. Tombesi, Phys. Lett. A, 213, 1 (1996).
V. V. Dodonov and V. I. Man’ko, Phys. Lett. A, 229, 335 (1997).
V. I. Man’ko and O. V. Man’ko, Zh. Éksp. Teor. Fiz, 112, 796 (1997) [J. Exp. Theor. Phys., 85, 430 (1997)].
O. V. Man’ko and V. I. Man’ko, J. Russ. Laser Res., 18, 407 (1997).
M. A. Man’ko, J. Russ. Laser Res., 22, 168 (2001).
M. A. Man’ko, V. I. Man’ko and R. Vilela Mendes, J. Russ. Laser Res., 27, 507 (2006).
E. H. Lieb and M. B. Ruskai, J. Math. Phys., 14, 1938 (1973).
A. E. Rastegin, Los Alamos ArXiv quant-ph/0807.2691 v1 (2008).
S. Wehner and A. Winter, Los Alamos ArXiv quant-ph/0907.3704 v1 (2009).
S. De Nicola, R. Fedele, M. A. Man’ko, and V. I. Man’ko, Eur. Phys. J. B, 52, 191 (2006).
M. A. Man’ko, J. Russ. Laser Res., 27, 405 (2006).
M. A. Man’ko, V. I. Man’ko, S. De Nicola, and R. Fedele, Acta Phys. Hung. B, 26, 71 (2006).
M. A. Man’ko, O. V. Man’ko, and V. I. Man’ko, Int. J. Mod. Phys. B, 20, 1399 (2006).
S. De Nicola, R. Fedele, M. A. Man’ko, and V. I. Man’ko, J. Phys. Conf. Ser., 70, 012007 (2007).
S. De Nicola, R. Fedele, M. A. Man’ko, and V. I. Man’ko, Theor. Math. Phys., 152, 1081 (2007).
M. A. Man’ko, “Tomographic entropy and new entropic uncertainty relations,” in: G. Adenier, A. Yu. Khrennikov, P. Lahti, V. I. Man’ko, and T. Nieuwenhuizen (eds.), Quantum Theory: Reconsideration of Foundations-4 (Vaxjo, Sweden, June 2007), AIP Conference Proceedings Series (2007), Vol. 962, p. 132.
M. A. Man’ko and V. I. Man’ko, Teor. Mat. Fiz., 160, 143 (2009) [Theor. Math. Phys., 160, 995 (2009)].
V. V. Dodonov and V. I. Man’ko, Invariants and the Evolution of Nonstationary Quantum Systems, Proceedings of the P. N. Lebedev Physical Institute, Nauka, Moscow (1987), Vol. 183 [translated by Nova Science, N.Y. (1989)].
V. I. Man’ko and R. V. Mendes, Phys. Lett. A, 263, 53 (1999).
I. Bialynicki-Birula, Phys. Rev. A, 74, 052101 (2006).
E. Schrödinger, Sitzungsber. Preuss. Acad. Wiss., 24, 296 (1930).
H. P. Robertson, Phys. Rev., 35, 667 (1930).
H. P. Robertson, Phys. Rev., 46, 794 (1934).
V. I. Man’ko, G. Marmo, E. C. G. Sudarshan, and F. Zaccaria, Phys. Lett. A, 327, 353 (2004).
O. V. Man’ko and V. I. Man’ko, J. Russ. Laser Res., 25, 115 (2004).
M. B. Ruskai, Los Alamos ArXiv quant-ph/0404126 v4 (2004).
Author information
Authors and Affiliations
Corresponding author
Additional information
Manuscript submitted by the author in English on October 19, 2009.
Rights and permissions
About this article
Cite this article
Man’ko, M.A. Quantum and classical inequalities for tomographic entropies. J Russ Laser Res 30, 514–524 (2009). https://doi.org/10.1007/s10946-009-9091-0
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10946-009-9091-0