Abstract
The probability-representation entropy (tomographic entropy) of an arbitrary quantum state is introduced. Using the properties of the spin tomogram as the standard probability-distribution function, the tomographic entropy notion is discussed. The relation of tomographic entropy to Shannon entropy and von Neumann entropy is elucidated.
Similar content being viewed by others
References
S. Mancini, V. I. Man'ko, and P. Tombesi, Phys. Lett. A, 213, 1 (1996).
Olga Man'ko and V. I. Man'ko, J. Russ. Laser Res., 18, 407 (1997).
V. V. Dodonov and V. I. Man'ko, Phys. Lett. A, 239, 335 (1997).
V. I. Man'ko and O. V. Man'ko, JETP, 85, 430 (1997).
O. V. Man'ko, V. I. Man'ko, and G. Marmo, Phys. Scr., 62, 446 (2000).
O. V. Man'ko, V. I. Man'ko, and G. Marmo, J. Phys. A: Math. Gen., 35, 699 (2002).
S. Mancini, O. V. Man'ko, V. I. Man'ko, and P. Tombesi, J. Phys. A: Math. Gen., 34, 3461 (2001).
A. B. Klimov, O. V. Man'ko, V. I. Man'ko, Yu. F. Smirnov, and V. N. Tolstoy, J. Phys. A: Math. Gen., 35, 6101 (2002).
V. A. Andreev, O. V. Man'ko, V. I. Man'ko, and S. S. Safonov, J. Russ. Laser Res., 19, 340 (1998).
O. V. Man'ko, V. I. Man'ko, and S. S. Safonov, Theor. Math. Phys., 115, 185 (1998).
V. I. Man'ko and S. S. Safonov, Yad. Fiz., 4, 658 (1998).
V. A. Andreev and V. I. Man'ko, JETP, 87, 239 (1998).
S. Weigert, Phys. Rev. Lett., 84, 802 (2000).
O. Castanos, R. Lopes-Pena, M. A. Man'ko, and V. I. Man'ko, J. Phys. A: Math. Gen., 36, 4677 (2003).
U. Leonhardt, Phys. Rev. A, 53, 2998 (1996).
E. C. Wenttsel, Probability Theory, Nauka, Moscow (1969), 4th ed.
S. Mancini, V. I. Man'ko, and P. Tombesi, Quantum Semiclass. Opt., 7, 615 (1995).
M. A. Man'ko, J. Russ. Laser Res., 22, 168 (2001); S. De Nicola, R. Fedele, M. A. Man'ko, and V. I. Man'ko, Eur. Phys. J. B, 36, 385 (2003).
C. E. Shannon, Bell Tech. J., 27, 379 (1948).
J. von Neumann, Matematische Grundlagen der Quantenmechanyk, Springer (1932).
A. S. Holevo, Statistical Structure of Quantum Theory, Lecture Notes in Physics, Springer (2001), Vol. 67; Russ. Math. Surveys, 53, No. 6, 1295 (1998).
V. I. Man'ko, G. Marmo, E. C. G. Sudarshan, and F. Zaccaria, J. Russ. Laser Res., 24, 507 (2003).
A. Stotland, A. A. Pomeransky, E. Bachmat, and D. Cohen, “The information entropy of quantum mechanical states,” Eprint quant-ph/040121.
D. Collins and S. Popescu, “Frames of reference and the intrinsic directional information of a particle with spin,” Eprint quant-ph/0401096.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Man'ko, O., Man'ko, V.I. Probability-Representation Entropy for Spin-State Tomogram. Journal of Russian Laser Research 25, 115–122 (2004). https://doi.org/10.1023/B:JORR.0000018981.06864.12
Issue Date:
DOI: https://doi.org/10.1023/B:JORR.0000018981.06864.12