Abstract
We obtain a new entropic inequality for quantum and tomographic Shannon information for systems of two qubits. We derive the inequality relating quantum information and spin-tomographic information for particles with spin j = 3/2. We recommend the method for obtaining new entropic and information inequalities for composite systems of qudits, as well as for one qudit.
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
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).
V. N. Chernega and V. I. Man’ko, J. Russ. Laser Res., 30, 359 (2009).
C. E. Shannon, Bell Syst. Tech. J, 27, 379 (1948).
E. H. Lieb and R. Seiringer, Phys. Rev. A, 71, 062329 (2005).
E. H. Lieb and M. B. Ruskai, J. Math. Phys., 14, 1938 (1973).
D. Petz, Rep. Math. Phys., 23, 57 (1986).
E. Carlen and E. H. Lieb, Am. Math. Soc. Trans., 189, 59 (1999).
A. Wehrl, Rep. Math. Phys., 16, 353 (1979).
M. B. Ruskai, J. Math. Phys., 43, 4358 (2002).
A. S. Holevo, Statistical Structure of Quantum Theory, Lecture Notes in Physics, Monographs, Springer (2001)
M. A. Man’ko and V. I. Man’ko, Found. Phys., 41, 330 (2011).
M. A. Man’ko, V. I. Man’ko, and R. V. Mendes, J. Russ. Laser Res., 27, 507 (2006).
M. A. Man’ko and V. I. Man’ko, “Quantum correlations expressed as information and entropic inequalities for composite and noncomposite systems,” Symmetries in Science XVI, Proceedings of the International Symposium of Symmetries in Science (Bregenz, Austria, July 2013), J. Phys.: Conf. Ser. (2014, in press).
M. A. Man’ko and V. I. Man’ko, “Quantum strong subadditivity condition for systems without subsystems,” Los Alamos arXiv:1312.6988 (2013); Phys. Scr. T (2014, in press).
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).
A. Ibort, V. I. Man’ko, G. Marmo, et al., Phys. Scr., 79, 065013 (2009).
M. A. Man’ko, V. I. Man’ko, G. Marmo, et al., “Introduction to tomography, classical and quantum,” Nuovo Cimento, Colloquia and Communications in Physics, Mathematical Structures in Quantum Systems and Applications (2013), Vol. 36, Ser. 3, p. 163.
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).
O. V. Man’ko, V. I. Man’ko, and G. Marmo, “Tomographic map within the framework of starproduct quantization’,” in: E. Kapuschik and A. Horzela (Eds.), Proceedings of the Second International Symposium on Quantum Theory and Symmetries (Krakow, 2001), World Scientific, Singapore (2001), p. 126.
O. V. Man’ko, V. I. Man’ko, G. Marmo, and P. Vitale, Phys. Lett. A, 360, 522 (2007).
M. A. Man’ko, V. I. Man’ko, and R. V. Mendes, J. Phys. A: Math. Gen., 34, 8321 (2001).
O. V. Manko and V. N. Chernega, JETP Lett., 97, 557 (2013).
V. N. Chernega, O. V. Man’ko, V. I. Man’ko, et al., J. Russ. Laser Res., 27, 132 (2006).
M. A. Man’ko and V. I. Man’ko, J. Russ. Laser Res., 34, 203 (2013).
V. I. Man’ko and A. Yurkevich, J. Russ. Laser Res., 34, 463 (2013).
I. H. Kim, Los Alamos arXiv:12105190 (2011).
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).
V. N. Chernega, O. V. Man’ko, and V. I. Man’ko, J. Russ. Laser Res., 34, 383 (2013).
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.), Symmetries in Science X, Proceedings of the International Symposium of Symmetries in Science (Bregenz, Austria, 1997), Plenum Publishers, New York (1998), p. 207.
O. V. Man’ko, J. Russ. Laser Res., 28, 483 (2007).
V. A. Andreev, O. V. Man’ko, V. I. Man’ko, and S. S. Safonov, J. Russ. Laser Res., 19, 340 (1998).
A. B. Klimov, O. V. Man’ko, V. I. Man’ko, et al., J. Phys. A: Math. Gen, 35, 6101 (2002).
O. V. Man’ko, Acta Phys. Hung. A, Heavy Ion Phys. Ser., 19/3-4, 313 (2004).
O. V. Man’ko and V. I. Man’ko, J. Phys.: Conf. Series, 36, 137 (2006).
O. V. Man’ko and V. I. Man’ko, Fortschr. Phys., 57, 1064 (2009).
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Chernega, V.N., Man’ko, O.V. Tomographic and Improved Subadditivity Conditions for Two Qubits and a Qudit with j = 3/2. J Russ Laser Res 35, 27–38 (2014). https://doi.org/10.1007/s10946-014-9397-4
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10946-014-9397-4