Abstract
A local orthogonal transformation that transforms any centrosymmetric density matrix of a two-qubit system to the X form has been found. A piecewise-analytic-numerical formula Q = min{Q π/2, Q θ, Q 0}, where Q π/2 and Q 0 are analytical expressions and the branch Q 0 θ can be obtained only by numerically searching for the optimal measurement angle θ ∈ (0, π/2), is proposed to calculate the quantum discord Q of a general X state. The developed approaches have been applied for a quantitative description of the recently predicted flickering (periodic disappearance and reappearance) of the quantum-information pair correlation between nuclear 1/2 spins of atoms or molecules of a gas (for example, 129Xe) in a bounded volume in the presence of a strong magnetic field.
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References
L. C. Céleri, J. Maziero, and R. M. Serra, Int. J. Quantum Inf. 9, 1837 (2011).
K. Modi, A. Brodutch, H. Cable, T. Paterek, and V. Vedral, Rev. Mod. Phys. 84, 1655 (2012).
S. M. Aldoshin, E. B. Fel’dman, and M. A. Yurishchev, Low Temp. Phys. 40(1), 3 (2014).
Y. Huang, New J. Phys. 16, 033027 (2014).
S. Luo, Phys. Rev. A: At., Mol., Opt. Phys. 77, 042303 (2008).
T. Yu and J. H. Eberly, Quantum Inf. Comput. 7, 459 (2007).
A. R. P. Rau, J. Phys. A: Math. Theor. 42, 0412002 (2009).
M. Ali, A. R. P. Rau, and G. Alber, Phys. Rev. A: At., Mol., Opt. Phys. 81, 042105 (2010); M. Ali, A. R. P. Rau, and G. Alber, Phys. Rev. A: At., Mol., Opt. Phys. 82, 069902(E) (2010).
F. F. Fanchini, T. Werlang, C. A. Brasil, G. E. Arruda, and A. O. Caldeira, Phys. Rev. A: At., Mol., Opt. Phys. 81, 052107 (2010).
B. Li, Z.-X. Wang, and S.-M. Fei, Phys. Rev. A: At., Mol., Opt. Phys. 83, 022321 (2011).
B.-F. Ding, X.-Y. Wang, and H.-P. Zhao, Chin. Phys. B 20, 100302 (2011).
X.-M. Lu, J. Ma, Z. Xi, and X. Wang, Phys. Rev. A: At., Mol., Opt. Phys. 83, 012327 (2011).
Q. Chen, C. Zhang, S. Yu, X. X. Yi, and C. H. Oh, Phys. Rev. A: At., Mol., Opt. Phys. 84, 042313 (2011).
Y. Huang, Phys. Rev. A: At., Mol., Opt. Phys. 88, 014302 (2013).
J. Baugh, A. Kleinhammes, D. Han, Q. Wang, and Y. Wu, Science (Washington) 294, 1505 (2001).
W. S. Warren, Science (Washington) 294, 1475 (2001).
E. B. Fel’dman and M. G. Rudavets, J. Exp. Theor. Phys. 98(2), 207 (2004).
A. V. Fedorova, E. B. Fel’dman, and D. E. Polianczyk, Appl. Magn. Reson. 35, 511 (2009).
J. Jeener, J. Chem. Phys. 134, 114519 (2011).
E. B. Fel’dman, G. B. Furman, and S. D. Goren, Soft Matter 8, 9200 (2012).
M. G. Rudavets, J. Magn. Reson. 230, 10 (2013).
E. B. Fel’dman, E. I. Kuznetsova, and M. A. Yurishchev, J. Phys. A: Math. Theor. 45, 475304 (2012).
D. Z. Rossatto, T. Werlang, E. I. Duzzioni, and C. J. Villas-Boas, Phys. Rev. Lett. 107, 153601 (2011).
J. R. Weaver, Am. Math. Mon. 92, 711 (1985).
Kh. D. Ikramov, Zh. Vychisl. Mat. Mat. Fiz. 33, 620 (1993).
A. Andrew, SIAM Rev. 40, 697 (1998).
E. S. Venttsel’, The Probability Theory (Nauka, Moscow, 1964) [in Russian].
V. P. Chistyakov, A Course of the Probability Theory (Nauka, Moscow, 1982) [in Russian].
G. Korn and T. Korn, Mathematical Handbook for Scientists and Engineers (McGraw-Hill, New York, 1968; Nauka, Moscow, 1984).
C. E. Shannon, The Mathematical Theory of Communication (University of Illinois, Chicago, United States, 1963; Inostrannaya Literatura, Moscow, 1963).
R. L. Stratonovich, The Theory of Information (Sovetskoe Radio, Moscow, 1975) [in Russian].
V. V. Panin, Fundamentals of the Theory of Information (BINOM, Moscow, 2007) [in Russian].
E. M. Gabidulin and N. I. Pilipchuk, Lectures on the Theory of Information (Moscow Engineering Physics Institute, Moscow, 2007) [in Russian].
A. S. Holevo, Introduction to the Quantum Information Theory (MTsNMO, Moscow, 2003) [in Russian].
A. S. Holevo, Quantum Systems, Channels, and Information: A Mathematical Introduction (MTsNMO, Moscow, 2010; Walter De Gruyter, Berlin, 2012).
M. A. Nielsen and I. L. Chuang, Quantum Computation and Quantum Information (Cambridge University Press, Cambridge, 2000; Mir, Moscow, 2006).
H. Ollivier and W. H. Zurek, Phys. Rev. Lett. 88, 017901 (2002).
M. A. Yurishchev, arXiv:1302.5239 [quant-ph].
L. Ciliberti, R. Rossignoli, and N. Canosa, Phys. Rev. A: At., Mol., Opt. Phys. 82, 042316 (2010).
M. A. Yurischev, arXiv:1404.5735 [quant-ph].
M. A. Yurishchev, Phys. Rev. B: Condens. Matter 84, 024418 (2011).
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Original Russian Text © M.A. Yurishchev, 2014, published in Zhurnal Eksperimental’noi i Teoreticheskoi Fiziki, 2014, Vol. 146, No. 5, pp. 946–956.
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Yurishchev, M.A. NMR dynamics of quantum discord for spin-carrying gas molecules in a closed nanopore. J. Exp. Theor. Phys. 119, 828–837 (2014). https://doi.org/10.1134/S106377611411020X
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DOI: https://doi.org/10.1134/S106377611411020X