Abstract
We obtain a new quantum entropic inequality for the states of a system of n ≥ 1 qudits. The inequality has the form of the quantum subadditivity condition of a bipartite qudit system and coincides with the subadditivity condition for the system of two qudits. We formulate a general statement on the existence of the subadditivity condition for an arbitrary probability distribution and an arbitrary qudit-system tomogram. We discuss the nonlinear quantum channels creating the entangled states from separable states.
Article PDF
Similar content being viewed by others
Explore related subjects
Discover the latest articles, news and stories from top researchers in related subjects.Avoid common mistakes on your manuscript.
References
C. E. Shannon, Bell Syst. Tech. J, 27, 379 (1948).
L. D. Landau, Z. Phys., 45, 430 (1927).
L. D. Landau and E. M. Lifshiz, Quantum Mechanics [in Russian], Nauka, Moscow (1963).
J. von Neumann, Nach. Ges. Wiss. G¨ottingen, 11, 245 (1927).
J. von Neumann, Mathematische Grundlagen der Quantenmechanik, Springer, Berlin (1932).
A. S. Holevo, Statistical Structure of Quantum Theory, Lecture Notes in Physics, Monographs, Springer (2001).
S. Mancini, V. I. Man’ko, and P. Tombesi, Phys. Lett. A, 213, 1 (1996).
O. V. 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, 229, 335 (1997).
V. I. Man’ko and O. V. Man’ko, J. Exp. Theor. Phys., 85, 430 (1997).
O. V. Man’ko, in: B. Gruber and H. Ramek (Eds.), Proceedings of the International Symposium on Symmetries in Science X, Bregenz, Austria, 1997 (Symmetries in Science X), Plenum Press, New York (1998), p. 207.
M. A. Man’ko and V. I. Man’ko, Found. Phys., 41, 330 (2011).
S. De Nicola, R. Fedele, M. A. Man’ko, and V. I. Man’ko, Phys. Scr., T135, 014053 (2009).
V. N. Chernega and V. I. Man’ko, AIP Conf. Proc., 1424, 33 (2012).
V. N. Chernega and V. I. Man’ko, Int. J. Quantum Inf., 10, 124101 (2012).
V. N. Chernega and V. I. Man’ko, J. Russ. Laser Res., 32, 125 (2011).
O.V. Manko and V. N. Chernega, JETP Lett., 97, 557 (2013).
M. A. Man’ko, V. I. Man’ko, G. Marmo, et al., J. Russ. Laser Res., 35, 79(2014).
M. A. Man’ko and V. I. Man’ko, Phys. Scr., T160, 014030 (2014).
V. N. Chernega and V. I. Man’ko, J. Russ. Laser Res., 28, 103 (2007).
C. Lupo, V. I. Man’ko, and G. Marmo, J. Phys. A: Math. Theor., 40, 13091 (2007).
E. H. Lieb and R. Seiringer, Phys. Rev. A, 71, 062329 (2005).
O. V. Manko and V. N. Chernega, J. Russ. Laser Res., 35, 27 (2014).
A. I. Khrennikov, Contextual Approach to Quantum Formalism, Springer (2009).
A. Khrennikov, arXiv:1204.5172v1 [quant-ph] (2012).
A. I. Khrennikov, Phys. A: Stat. Mech. Appl., 393, 207 (2014).
W. F. Stinespring, “Positive functions on C*-algebras,” Proc. Amer. Math. Soc. (1955), p. 211.
E. C. G. Sudarshan, P. M. Mathews, and J. Rau, Phys. Rev., 121, 920(1961).
M. A. Man’ko, V. I. Man’ko, G. Marmo, et al., Nuovo Cimento C, 36, Ser. 3, 163 (2013).
Author information
Authors and Affiliations
Corresponding author
Additional information
Manuscript submitted by the authors in English on March 14, 2014.
Rights and permissions
About this article
Cite this article
Chernega, V.N., Man’ko, O.V. & Man’ko, V.I. Subadditivity Condition for Spin Tomograms and Density Matrices of Arbitrary Composite and Noncomposite Qudit Systems. J Russ Laser Res 35, 278–290 (2014). https://doi.org/10.1007/s10946-014-9424-5
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10946-014-9424-5