Quantum entanglement and quantum discord in magnetoactive materials (Review Article)

The conceptions of quantum entanglement and quantum discord are reviewed. The entropic measures for these informational correlations are presented. The examples which demonstrate the presence of quantum information correlations in different paramagnetic materials with ferro- and antiferromagnetic couplings are given. The temperature behavior of the discord for atomic nuclear spins is considered. The decoherence of quantum states with electron and nuclear spins is discussed.

PACS: 03.65.Ud Entanglement and quantum nonlocality;
PACS: 03.67.Mn Entanglement measures, witnesses, and other characterizations;
PACS: 75.10.Jm Quantum spin models;
PACS: 75.50.Xx Molecular magnets.

Key words: qubit, decoherence time, density matrix, entropy, information correlation.

References

1. A. S. Holevo, An Introduction to Quantum Information Theory (Moscow Center of Continuous Mathematical Education (MCCME), Moscow, 2002) [in Russian]. Google Scholar

2. L. Amico, R. Fazio, A. Osterloh, and V. Vedral, Rev. Mod. Phys. 80, 517 (2008). CrossRef Google Scholar

3. R. Horodecki, P. Horodecki, M. Horodecki, and K. Horodecki, Rev. Mod. Phys. 81, 865 (2009). CrossRef Google Scholar

4. A. S. Holevo, Quantum Systems, Channels, Information (Moscow Center of Continuous Mathematical Education (MCCME), Moscow, 2010) [in Russian]. Google Scholar

5. K. A. Valiev and A. A. Kokin, Quantum Computers: Expectations and Reality (Institute of Computer Science, Moscow-Izhevsk, 2002) [in Russian]. Google Scholar

6. A. A. Kokin, Solid State Quantum Computers Based on Nuclear Spins (Institute of Computer Science, Moscow-Izhevsk, 2004) [in Russian]. Google Scholar

7. K. A. Valiev, Usp. Fiz. Nauk 175, 3 (2005) CrossRef Google Scholar

8. M. A. Nielsen and I. L. Chuang, Quantum Computation and Quantum Information (Cambridge University Press, Cambridge (2000). Google Scholar

9. W. H. Zurek, Ann. Phys. (Leipzig) 9, 855 (2000). CrossRef Google Scholar

10. L. Henderson and V. Vedral, J. Phys. A: Math. Gen. 34, 6899 (2001). CrossRef Google Scholar

11. H. Ollivier and W. H. Zurek, Phys. Rev. Lett. 88, 017901 (2002). Google Scholar

12. V. Vedral, Phys. Rev. Lett. 90, 050401 (2003). CrossRef Google Scholar

13. W. H. Zurek, Phys. Rev. A 67, 012320 (2003). CrossRef Google Scholar

14. E. Knill and R. Laflamme, Phys. Rev. Lett. 81, 5672 (1998). CrossRef Google Scholar

15. A. Datta, A. Shaji, and C. M. Caves, Phys. Rev. Lett. 100, 050502 (2008). CrossRef Google Scholar

16. B. P. Lanyon, M. Barbieri, M. P. Almeida, and A. G. White, Phys. Rev. Lett. 101, 200501 (2008). CrossRef Google Scholar

17. R. Dillenschneider, Phys. Rev. B 78, 224413 (2008). CrossRef Google Scholar

18. M. S. Sarandy, Phys. Rev. A 80, 022108 (2009). CrossRef Google Scholar

19. T. Werlang, C. Trippe, G. A. P. Ribeiro, and G. Rigolin, Phys. Rev. Lett. 105, 095702 (2010). CrossRef Google Scholar

20. T. Werlang, G. A. P. Ribeiro, and G. Rigolin, Int. J. Mod. Phys. B 27, 1345032 (2013). CrossRef Google Scholar

21. A. Ferraro, L. Aolita, D. Cavalcanti, F. M. Cucchietti, and A. Acín, Phys. Rev. A 81, 052318 (2010). CrossRef Google Scholar

22. V. Madhok and A. Datta, Int. J. Mod. Phys. B 27, 1345041 (2013). CrossRef Google Scholar

23. B. Dakić, Y.-O. Lipp, X.-S. Ma, M. Ringbauer, S. Kroatschek, S. Barz, T. Paterek, V. Vedral, A. Zeilinger, Č. Brukner, and P. Walther, Nature Phys. 8, 666 (2012). CrossRef Google Scholar

24. M. Gu, H. M. Chrzanowski, S. M. Assad, T. Symul, K. Modi, T. C. Ralph, V. Vedral, and P. K. Lam, Nature Phys. 8, 671 (2012). CrossRef Google Scholar

25. L. C. Céleri, J. Maziero, and R. M. Serra, Int. J. Quantum Inf. 9, 1837 (2011). CrossRef Google Scholar

26. K. Modi, A. Brodutch, H. Cable, T. Paterek, and V. Vedral, Rev. Mod. Phys. 84, 1655 (2012). CrossRef Google Scholar

27. L. Amico, S. Bose, V. E. Korepin, and V. Vedral (guest editors) “ Special issue: Classical versus quantum correlations in composite systems,” Int. J. Mod. Phys. B 27, 1–3 (2013). Google Scholar

28. E. S. Wentzel, Probability Theory (First Steps) (Nauka, Moscow, 1964) [(Mir Publishers, Moscow, 1975)]. Google Scholar

29. V. P. Chistyakov, Course in Probability Theory (Nauka, Moscow, 1982) [in Russian]. Google Scholar

30. G. A. Korn and T. M. Korn, Mathematical Handbook for Scientists and Engineers: Definitions, Theorems, and Formulas for Reference and Review (McGraw-Hill, New York, 1961). Google Scholar

31. W. K. Wootters, Quantum Inf. Comput. 1, 27 (2001). Google Scholar

32. M. B. Plenio and S. Virmani, Quantum Inf. Comput. 7, 1 (2007). Google Scholar

33. L. Bombelli, R. K. Koul, J. Lee, and R. D. Sorkin, Phys. Rev. D 34, 373 (1986). CrossRef Google Scholar

34. C. H. Bennett, G. Brassard, S. Popescu, B. Schumacher, J. Smolin, and W. K. Wootters, Phys. Rev. Lett. 76, 722 (1996). CrossRef Google Scholar

35. C. H. Bennett, H. J. Bernstein, S. Popescu, and B. Schumacher, Phys. Rev. A 53, 2046 (1996). CrossRef Google Scholar

36. C. H. Bennett, D. P. DiVincenzo, J. A. Smolin, and W. K. Wootters, Phys. Rev. A 54, 3824 (1996). CrossRef Google Scholar

37. I. V. Bargatin, B. A. Grishanin, and V. N. Zadkov, Usp. Fiz. Nauk 171, 625 (2001) CrossRef Google Scholar

38. P. Calabrese and J. Cardy, J. Stat. Mech. 2004, P06002. Google Scholar

39. P. Calabrese and J. Cardy, J. Quantum Inf. 4, 429 (2006). CrossRef Google Scholar

40. I. Peschel, J. Stat. Mech. 2004, P12005. CrossRef Google Scholar

41. I. Peschel and V. Eisler, J. Phys. A: Math. Theor. 42, 504003 (2009). CrossRef Google Scholar

42. M. A Yurishchev, Zh. Eksp. Teor. Fiz. 138, 595 (2010) M. A Yurishchev, J. Exp. Theor. Phys. 111, 525 (2010)]. CrossRef Google Scholar

43. G. Vidal, J. I. Latorre, E. Rico, and A. Kitaev, Phys. Rev. Lett. 90, 227902 (2003). CrossRef Google Scholar

44. R. F. Werner, Phys. Rev. A 40, 4277 (1989). CrossRef Google Scholar

45. A. Peres, Phys. Rev. Lett. 77, 1413 (1996). CrossRef Google Scholar

46. S. Hill and W. K. Wootters, Phys. Rev. Lett. 78, 5022 (1997). CrossRef Google Scholar

47. W. K. Wootters, Phys. Rev. Lett. 80, 2245 (1998). CrossRef Google Scholar

48. K. Audenaert, F. Verstraete, and B. De Moor, Phys. Rev. A 64, 052304 (2001). CrossRef Google Scholar

49. B. Bleaney and K. D. Bowers, Proc. R. Soc. London, Ser. A 214, 451 (1952). CrossRef Google Scholar

50. R. L. Carlin, Magnetochemistry (Springer-Verlag, Berlin, 1986). Google Scholar

51. M. A. Nielsen, “ Quantum information theory,” Ph.D. dissertation (The University of New Mexico, 1998); e-print arXiv:quant-ph/0011036. CrossRef Google Scholar

52. M. C. Arnesen, S. Bose, and V. Vedral, Phys. Rev. Lett. 87, 017901 (2001). CrossRef Google Scholar

53. A. E Dubinov, I. D. Dubinova, and S. K. Saikov, W-Lambert function: Tables of Integrals and Other Mathematical Properties (SarFTI, Sarov, 2004) [in Russian]. Google Scholar

54. M. Wieśniak, V. Vedral, and Č. Brukner, New J. Phys. 7, 258 (2005). CrossRef Google Scholar

55. M. Wieśniak, “ Quantum entanglement in some physical systems,” Ph.D. dissertation (University of Gdańsk, 2007); e-print arXiv:quant-ph/0710.1775. CrossRef Google Scholar

56. Č. Brukner, V. Vedral, and A. Zeilinger, Phys. Rev. A 73, 012110 (2006). CrossRef Google Scholar

57. A. M. Souza, M. S. Reis, D. O. Soares-Pinto, L. S. Oliveira, and R. S. Sarthour, Phys. Rev. B 77, 104402 (2008). CrossRef Google Scholar

58. M. A. Yurishchev, Phys. Rev. B 84, 024418 (2011). CrossRef Google Scholar

59. S. M. Aldoshin, A. I. Zenchuk, E. B. Fel'dman, and M. A. Yurishchev, Usp. Khim. 81, 91 (2012) CrossRef Google Scholar

60. S. M. Aldoshin, E. B. Fel'dman, and M. A. Yurishchev, Zh. Éksp. Teor. Fiz. 134, 940 (2008) S. M. Aldoshin, E. B. Fel'dman, and M. A. Yurishchev, J. Exp. Theor. Phys. 107, 804. (2008)]. CrossRef Google Scholar

61. N. A. Sanina, S. M. Aldoshin, T. N. Rudneva, N. I. Golovina, G. V. Shilov, Y. M. Sul'ga, N. S. Ovanesyan, V. N. Ikorskii, and V. I. Ovcharenko, J. Mol. Struct. 752, 110 (2005). CrossRef Google Scholar

62. N. A. Sanina, T. N. Rudneva, S. M. Aldoshin, A. N. Chekhlov, R. B. Morgunov, E. V. Kurganova, and N. S. Ovanesyan, Izv. Akad. Nauk, Ser. Khim. 1, 28 (2007) N. A. Sanina, T. N. Rudneva, S. M. Aldoshin, A. N. Chekhlov, R. B. Morgunov, E. V. Kurganova, and N. S. Ovanesyan, Russ. Chem. Bull., Int. Ed. 56, 28 (2007)]. CrossRef Google Scholar

63. A. F. Vanin, Usp. Fiz. Nauk 170, 455 (2000) CrossRef Google Scholar

64. A. F. Shestakov, Yu. M. Shul'ga, N. S. Emel'yanova, N. A. Sanina, and S. M. Aldoshin, Izv. Akad. Nauk, Ser. Khim. 7, 1244 (2007) A. F. Shestakov, Yu. M. Shul'ga, N. S. Emel'yanova, N. A. Sanina, and S. M. Aldoshin, Russ. Chem. Bull., Int. Ed. 56, 1289 (2007)]. CrossRef Google Scholar

65. A. N. Vasil'ev, M. M. Markina, and E. A. Popova, Fiz. Nizk. Temp. 31, 272 (2005); A. N. Vasil'ev, M. M. Markina, and E. A. Popova, Low Temp. Phys. 31, 203 (2005)]. CrossRef Google Scholar

66. A. I. Smirnov and V. N. Glazkov, Zh. Éksp. Teor. Fiz. 132, 984 (2007) A. I. Smirnov and V. N. Glazkov, J. Exp. Theor. Phys. 105, 861 (2007)]. CrossRef Google Scholar

67. C. E. Shannon, Collected Works on Information Theory and Cybernetics (IL, Moscow, 1963) [Russian translation]. Google Scholar

68. A. M Yaglom and I. M Yaglom, Probability and information (KomKniga, Moscow, 2006). Google Scholar

69. R. L Stratonovich, Information Theory (Sov. Radio, Moscow, 1975) [in Russian]. Google Scholar

70. V. V. Mityugov, Physical Basis of Information Theory (Sov. Radio, Moscow, 1976) [in Russian]. Google Scholar

71. V. V. Panin, Foundations of Information Theory (BINOM—Knowledge Laboratory, Moscow, 2007) [in Russian]. Google Scholar

72. E. M. Gabidulin and N. I. Pilipchuk, Lectures on Information Theory (MIFI, Moscow, 2007) [in Russian]. Google Scholar

73. J. Preskill, Quantum Information and Quantum Computation (SRC Regular and Chaotic Dynamics, Moscow-Izhevsk, 2008) J. Preskill, [Lecture Notes for Physics 229: Quantum Information and Computation (CalTec, 1998)] [Russian translation]. Google Scholar

74. S. Ya. Kilin, Usp. Fiz. Nauk 169, 507 (1999) CrossRef Google Scholar

75. A. Yu. Khrennikov, Introduction to Quantum Information Theory (Nauka, Fizmatlit, Moscow, 2008) [in Russian]. Google Scholar

76. S. Imre and F. Balázs, Quantum Computing and Communications: An Engineering Approach (Wiley, Chichester, 2005). Google Scholar

77. Quantum Theory and Measurements, edited by J. A. Wheeler and W. H. Zurek (Princeton University Press, Princeton, 1983). Google Scholar

78. A. S. Holevo, Probabilistic and Statistical Aspects of Quantum Theory (Nauka, Moscow, 1980) [(North Holland, Amsterdam, 1982)]. Google Scholar

79. S. Luo, Phys. Rev. A 77, 042303 (2008). CrossRef Google Scholar

80. F. F. Fanchini, T. Werlang, C. A. Brasil, L. G. E. Arruda, and A. O. Caldeira, Phys. Rev. A 81, 052107 (2010). CrossRef Google Scholar

81. M. Ali, A. R. P. Rau, and G. Alber, Phys. Rev. A 81, 042105 (2010); CrossRef Google Scholar

82. M. Ali, J. Phys. A: Math. Theor. 43, 495303 (2010). CrossRef Google Scholar

83. B. Li, Z.-X. Wang, and S.-M. Fei, Phys. Rev. A 83, 022321 (2011). CrossRef Google Scholar

84. D. Girolami and G. Adesso, Phys. Rev. A 83, 052108 (2011). CrossRef Google Scholar

85. M. A. Yurishchev, e-print arXiv:1302.5239[quant-ph]. CrossRef Google Scholar

86. J. R. Weaver, Am. Math. Mon. 92, 711 (1985). CrossRef Google Scholar

87. Kh. D. Ikramov, Zh. Vychiscl. Mat. Mat. Fiz. 33, 620 (1993) [in Russian]. Google Scholar

88. A. Andrew, SIAM Rev. 40, 697 (1998). CrossRef Google Scholar

89. D. A. Tennant, S. E. Nagler, A. W. Garrett, T. Barnes, and C. C. Torardi, Phys. Rev. Lett. 78, 4998 (1997). CrossRef Google Scholar

90. J. T. Haraldsen, T. Barnes, and J. L. Musfeldt, Phys. Rev. B 71, 064403 (2005). CrossRef Google Scholar

91. M. B. Stone, W. Tian, M. D. Lumsden, G. E. Granroth, D. Mandrus, J.-H. Chung, N. Harrison, and S. E. Nagler, Phys. Rev. Lett. 99, 087204 (2007). CrossRef Google Scholar

92. G. Xu, C. Broholm, D. H. Reich, and M. A. Adams, Phys. Rev. Lett. 84, 4465 (2000). CrossRef Google Scholar

93. S. A. Friedberg and C. A. Raquet, J. Appl. Phys. 39, 1132 (1968). CrossRef Google Scholar

94. J. C. Bonner, S. A. Friedberg, H. Kobayashi, D. L. Meier, and H. W. J. Blöte, Phys. Rev. B 27, 248 (1983). CrossRef Google Scholar

95. M. E. Fisher, The Nature of Critical Points (University of Colorado Press, Boulder, 1965). Google Scholar

96. L. Berger, S. A. Friedberg, and J. T. Schriempf, Phys. Rev. 132, 1057 (1963). CrossRef Google Scholar

97. B. N. Figgis and R. L. Martin, J. Chem. Soc., London 1956, 3837. Google Scholar

98. M. Fondo, A. M. García-Deibe, J. Sanmartin, M. R. Bermejo, L. Lezama, and T. Rojo, Eur. J. Inorg. Chem. 2003, 3703. CrossRef Google Scholar

99. E. I. Kuznetsova and M. A. Yurishchev, Quantum Inf. Proc. 12, 3587 (2013). CrossRef Google Scholar

100. G. E. Pake, J. Chem. Phys. 16, 327 (1948). CrossRef Google Scholar

101. A. Abragam, The Principles of Nuclear Magnetism (Oxford University Press, Oxford, 1961) Google Scholar

102. R. Auccaise, J. Maziero, L. C. Céleri, D. O. Soares-Pinto, E. R. de Azevedo, T. J. Bonagamba, R. S. Sarthour, I. S. Oliveira, and R. M. Serra, Phys. Rev. Lett. 107, 070501 (2011). CrossRef Google Scholar

103. G. Passante, O. Moussa, D. A. Trottier, and R. Laflamme, Phys. Rev. A 84, 044302 (2011). CrossRef Google Scholar

104. H. Katiyar, S. S. Roy, T. S. Mahesh, and A. Patel, Phys. Rev. A 86, 012309 (2012). CrossRef Google Scholar

105. H. S. Gutowsky, G. B. Kistiakowsky, G. E. Pake, and E. M. Purcell, J. Chem. Phys. 17, 972 (1949). CrossRef Google Scholar

106. H. Günther, NMR Spectroscopy: An Introduction (John Wiley and Sons, New York, 1980). Google Scholar

107. The Physics of Quantum Information, edited by D. Bouwmeester, A. Eckert, and A. Zeilinger (Springer-Verlag, Heidelberg, 2001). Google Scholar

108. T. D. Ladd, F. Jelezko, R. Laflamme, Y. Nakamura, C. Monroe, and J. L. O'Brien, Nature 464, 45 (2010). CrossRef Google Scholar

109. M. B. Mensky, Usp. Fiz. Nauk 173, 1199 (2003) CrossRef Google Scholar

110. H. G. Krojanski and D. Suter, Phys. Rev. Lett. 93, 090501 (2004). CrossRef Google Scholar

111. S. I. Doronin, E. B. Fel'dman, and A. I. Zenchuk, J. Chem. Phys. 134, 034102 (2011). CrossRef Google Scholar

112. L. M. K. Vandersypen and I. L. Chuang, Rev. Mod. Phys. 76, 1037 (2004). Google Scholar

113. I. S. Oliveira, T. J. Bonagamba, R. S. Sarthour, J. C. C. Freitas, and E. R. deAzevedo, NMR Quantum Information Processing (Elsevier, Amsterdam, 2007). Google Scholar

114. P. Cappellaro, C. Ramanathan, and D. G. Cory, Phys. Rev. A 76, 032317 (2007). CrossRef Google Scholar

115. J. J. L. Morton, A. M. Tyryshkin, A. Ardavan, K. Porfyrakis, S. A. Lyon, and G. A. D. Briggs, J. Chem. Phys. 124, 014508 (2006). CrossRef Google Scholar

116. E. M. Gauger, E. Rieper, J. J. L. Morton, S. C. Benjamin, and V. Vedral, Phys. Rev. Lett. 106, 040503 (2011). CrossRef Google Scholar

117. G. Balasubramanian, P. Neumann, D. Twitchen, M. Markham, R. Kolesov, N. Mizuochi, J. Isoya, J. Achard, J. Beck, J. Tissler, V. Jacques, P. R. Hemmer, F. Jelezko, and J. Wrachtrup, Nature Mater. 8, 383 (2009). CrossRef Google Scholar