Abstract
We study quantum correlations on the example of a bipartite system of two qubits. The system is described by the density matrix corresponding either to the Werner state or a generic X state. Also we study an analogous density matrix for the single-qudit state of a four-level atom. We perform the global unitary transform, calculate the quantum mutual information, and investigate its dependence on the parameters of the unitary matrix. Also we discuss the process of transforming a separable state into the entangled state for the composite system of two qubits and a single qudit.
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References
E. H. Lieb and M. B. Ruskai, J. Math. Phys., 14, 1938 (1973).
M. A. Nielsen and D. Petz, “A simple proof of the strong subadditivity inequality,” arXiv:0408130 [quant-ph] (2005).
M. B. Ruskai, “Liebs simple proof of concavity (A,B) > TrA p K † B 1−p K and remarks on related inequalities,” arXiv:0404126v1 [quant-ph] (2004).
H. Araki and E. H. Lieb, Commun. Math. Phys., 18, 160 (1970).
E. H. Lieb, Bull. Am. Math. Soc., 81, 1 (1975).
M. B. Ruskai, J. Math. Phys., 43, 4358 (2002); erratum 46, 019901 (2005).
J. von Neumann, Mathematical Foundations of Quantum Mechanics (1932), Translated by R. T. Beyer, Princeton University Press, Princeton (1955).
M. A. Man’ko and V. I. Man’ko, Phys. Scr., 2014, 014030 (2014).
Todd Tilma, Mark S. Byrd, and E. C. G. Sudarshan, J. Phys. A: Math. Gen., 35, 10445 (2002).
E. Schr¨odinger, Naturwissenschaften, 23, 807; 823; 844 (1935).
A. Einstein, B. Podolsky, and N. Rosen, Phys. Rev., 44, 777 (1935).
V. I. Man’ko and O. V. Man’ko, J. Exp. Theor. Phys., 85, 430 (1997).
V. I. Man’ko and L. A. Markovich, J. Russ. Laser Res., 35, 200 (2014).
M. A. Man’ko and V. I. Man’ko, Entropy, 17, 2876 (2015).
V. N. Chernega and O. V. Man’ko, Phys. Scr., 90, 074052 (2015).
J. F. Clauser, M. A. Horne, A. Shimony, and R. A. Holt, Phys. Rev. Lett. 24, 549 (1970).
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Manuscript submitted by the authors in English first on June 11, 2015 and in final form on August 2, 2015.
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Avanesov, A.S., Man’ko, V.I. Unitary Transform and Subadditivity Condition for Composite and Noncomposite Systems. J Russ Laser Res 36, 430–439 (2015). https://doi.org/10.1007/s10946-015-9520-1
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DOI: https://doi.org/10.1007/s10946-015-9520-1