Abstract
We discuss the notions of mutual information and conditional information for noncomposite systems, classical and quantum; both the mutual information and the conditional information are associated with the presence of hidden correlations in the state of a single qudit. We consider analogs of the entanglement phenomena in the systems without subsystems related to strong hidden quantum correlations.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
A. N. Kolmogorov, Foundations of the Theory of Probability, 2nd ed., Chelsea Publishing Company, New York (1956).
A. S. Holevo, Probabilistic and Statistical Aspects of Quantum Theory, North-Holland, Amsterdam (1982).
M. A. Nielsen and I. L. Chuang, Quantum Computation and Quantum Information, Cambridge University Press, Cambridge, UK (2000).
L. D. Landau, Z. Phys., 45, 430 (1927).
J. von Neumann, Göttingenische Nachrichten, 11 (Nov. 1927), S. 245–272.
J. von Neumann, Mathematische Grundlagen der Quantummechanik, Springer, Berlin (1932).
M. Asorey, A. Ibort, G. Marmo, and F. Ventriglia, Phys. Scr., 90, 074031 (2015).
M. A. Man’ko and V. I. Man’ko, J. Russ. Laser Res., 34, 203 (2013).
M. A. Man’ko, Phys. Scr., T153, 014045 (2013).
M. A. Man’ko and V. I. Man’ko, J. Phys.: Conf. Ser., 442, 012008 (2013).
M. A. Man’ko, V. I. Man’ko, G. Marmo, et al., Nuovo Cimento C, 36, 163 (2013).
M. A. Man’ko and V. I. Man’ko, J. Phys.: Conf. Ser., 538, 012016 (2014).
M. A. Man’ko and V. I. Man’ko, J. Russ. Laser Res., 35, 509 (2014).
M. A. Man’ko and V. I. Man’ko, Int. J. Quantum Inform., 12, 156006 (2014).
P. Adam, V. A. Andreev, J. Janszky, et al., Phys. Scr., T160, 014001 (2014).
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).
M. A. Man’ko and V. I. Man’ko, J. Russ. Laser Res., 35, 298 (2014).
M. A. Man’ko and V. I. Man’ko, J. Russ. Laser Res., 35, 509 (2014)
M. A. Man’ko and V. I. Man’ko, J. Russ. Laser Res., 35, 582 (2014).
M. A. Man’ko and V. I. Man’ko, J. Russ. Laser Res., 36, 301 (2015).
M. A. Man’ko and V. I. Man’ko, Entropy, 17, 2876 (2015).
M. A. Man’ko and V. I. Man’ko, J. Phys.: Conf. Ser., 698, 012004 (2016).
M. A. Man’ko, V. I. Man’ko, and G. Marmo, Nuovo Cimento C, 38, 167 (2016).
A. A. Klyachko, M. A. Can, S. Binicioˇglu, and A. S. Shumovsky, Phys. Rev. Lett., 101, 020403 (2008).
A. Figueroa, J. Lopez, O. Casta˜nos, et al., J. Phys. A: Math. Theor., 48, 065301 (2015).
M. Horodecki and J. Oppenheim, Nature Commun., 4, 2059 (2013).
J. Goold, M. Huber, A. Riera, et al., J. Phys. A: Math. Theor., 49, 143001 (2016).
J. A. López-Saldívar, O. Castaños, M. A. Man’ko, and V. I. Man’ko, “New entropic inequalities for qubit and unimodal Gaussian states,” Eur. Phys. Lett. (2017, submitted).
P. Facchi, G. Garnero, and M. Ligabo, “Quantum fluctuation relations,” arXiv:1705.06096 [quantph].
P. Facchi and G. Garnero, “Quantum thermodynamics and canonical typicality,” arXiv:1705.02270 [quant-ph].
V. I. Man’ko and Zh. Seilov, J. Russ. Laser Res., 38, 50 (2017).
V. N. Chernega, O. V. Man’ko, V. I. Man’ko, and Zh. Seilov, “New information and entropic inequalities for Clebsch–Gordan coefficients,” arXiv:1606.00854v4 [quant-ph]; Theor. Math. Phys. (2017, in press).
A. D. Pasquale, “Bipartite entanglement of large quantum systems,” arXiv:1206.6749v2 [quant-ph].
A. D. Pasquale, P. Facchi, V. G. Giovannetti, et al., J. Phys. A: Math. Theor., 45, 015308 (2012).
A. Peres, Phys. Rev. Lett., 77, 1413 (1996).
M. Horodecki, P. Horodecki, and R. Horodecki, Phys. Lett. A, 223, 1 (1996).
A. K. Fedorov, E. O. Kiktenko, O. V. Man’ko, and V. I. Man’ko, Phys. Rev. A, 91, 042312 (2015).
E. O. Kiktenko, A. K. Fedorov, A. A. Strakhov, and V. I. Man’ko, Phys. Lett. A, 379, 1409 (2015).
E. Glushkov, A. Glushkova, and V. I. Man’ko, J. Russ. Laser Res., 36, 448 (2015).
I. Ya. Doskoch and M. A. Man’ko, J. Russ. Laser Res., 36, 503 (2015).
M. A. Man’ko and V. I. Man’ko, J. Russ. Laser Res., 37, 1 (2016).
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Man’ko, M.A. Conditional Information and Hidden Correlations in Single-qudit States. J Russ Laser Res 38, 211–222 (2017). https://doi.org/10.1007/s10946-017-9636-6
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10946-017-9636-6