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Classical and Quantum Information

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Book cover Isotope-Based Quantum Information

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Abstract

Before studying the new aspects that quantum mechanics adds to information theory below, we will have a brief look at the basics of classical information theory in the next section. Information theory is a branch of applied mathematics and electrical engineering involving the quantification of information.

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Notes

  1. 1.

    As is well known [9], in 1961, Landauer had the important insight that there is a fundamental asymmetry in nature that allows us to process information. Copying classical information can be done reversibly and without wasting any energy, but when information is erased there is always an energy cost of kT ln 2 per classical bit to be paid ( for more details see, also [36]). Furthermore, an amount of heat equal to kT ln 2 is damped in the environment at the end of the erasing process. Landauer conjectured that this energy/entropy cost cannot be reduced below this limit irrespective of how the information is encoded and subsequently erased—it is a fundamental limit. Landauer’s discovery is important both theoretically and practically, as on the one hand, it relates the concept of information to physical quantities like thermodynamical entropy and free energy, and on the other hand, it may force the future designers of quantum devices to take into account the heat production caused by the erasure of information although this effect is tiny and negligible in today’s technology. At the same time, Landauer’s profound insight has led to the resolution of the problem of Maxwell’s demon by Bennett [37, 38]. By the way, for the first time the physical relation between entropy and information was done by Szilard at the investigation of the task of the Maxwell’s demon [30, 31]. On the other hand, mathematical definition of the information was introduced by Hartley in 1928 [11] and more elaboration on this definition was done by Shannon [1].

References

  1. C.E. Shannon, A mathematical theory of communications. Bell Syst. Techn. J. 27(379–423), 623–656 (1948)

    MathSciNet  Google Scholar 

  2. L. Brillouin, Science and Information Theory (Academic Press, New York, 1962)

    MATH  Google Scholar 

  3. T.M. Cover, J.A. Thomas, Elements of Information Theory (Chichester (J. Wiley& Sons, New York, 1991)

    Book  Google Scholar 

  4. E.T. Jaynes, Information Theory and statistical mechanics. Phys. Rev. 106, 620–630 (1957)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  5. E.T. Jaynes, Information Theory and statistical mechanics. II. Phys. Rev. 108, 171–190 (1957)

    MathSciNet  ADS  Google Scholar 

  6. A.N. Kolomogorov, The theory of information transmission. Izv. Akad. Nauk (Moscow) (1957), pp. 66–99 (in Russian)

    Google Scholar 

  7. A.N. Kolomogorov, Three approaches to the quantitative definition of information. Probl. Inform. Transmission 1, 4–7 (1965)

    Google Scholar 

  8. B.B. Kadomtsev, Dynamics and information (UFN, Moscow, 1999). (in Russian)

    Google Scholar 

  9. V.G. Plekhanov, Isotope-based quantum information, ArXiv: quant - ph/0909.0820 (2009)

    Google Scholar 

  10. V.G. Plekhanov, Quantum information and quantum computation. Trans. Computer Sci. College (N 1), Tallinn 2004, pp. 161–284. (in Russian)

    Google Scholar 

  11. R.V.L. Hartley, Transmission of Information. Bell Syst. Techn. J. 7, 535–563 (1928)

    Google Scholar 

  12. V.G. Plekhanov, Fundamentals and applications of isotope effect in solids. Prog. Mat. Sci. 51, 287–426 (2006)

    Article  Google Scholar 

  13. V.G. Plekhanov, L.M. Zhuravleva, Isotoptronics in medicine, geology and quantum information. Nanoindustry (Moscow) 1, 52–54 (2010) (in Russian)

    Google Scholar 

  14. C.H. Bennett, H.J. Bernstein, S. Popescu et al., Concentrating partial entanglement by local operations. Phys. Rev. A53, 2046–2052 (1996)

    ADS  Google Scholar 

  15. C. Witte, M. Trucks, A new entanglement measure induced by the Hilbert-Schmidt norm, ArXiv: quant - ph/9811027 (1998)

    Google Scholar 

  16. J.P. Paz, A.J. Roncaglia, Entanglement dynamics during decoherence, ArXiv:quant - ph/ 0909.0423 (2009)

    Google Scholar 

  17. C. Brukner, M. Zukowski, A. Zeilinger, The essence of entanglement, ArXiv: quant-ph/0106119 (2001)

    Google Scholar 

  18. T.E. Tessier, Complementarity and entanglement in quantum information theory. The University of New Mexico, Ph. D.Thesis in Physics, (2004)

    Google Scholar 

  19. M. Avellino, Entanglement and quantum information transfer in arrays of interacting systems, Ph. D. Thesis, University of London (2009)

    Google Scholar 

  20. K.-A.B. Soderberg, C. Monroe, Phonon-mediated entanglement for trapped ion quantum computing. Rep. Prog. Phys. 73, 036401–24 (2010)

    Article  ADS  Google Scholar 

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

    MATH  Google Scholar 

  22. O. Morsch, Quantum Bits and Quantum Secrets: How Quantum Physics Revolutionizing Codes and Computers (Wiley - VCH, Weinham, 2008)

    MATH  Google Scholar 

  23. P.A.M. Dirac, The Principles of Quantum Mechanics (Oxford University Press, Oxford, 1958)

    MATH  Google Scholar 

  24. R.P. Feynman, R.P. Leighton, M. Sands, The Feynman Lecture in Physics, vol. 3 (Addison-Wesley, Reading, MA, 1965)

    Google Scholar 

  25. L.D. Landau, E.M. Lifshitz, Quantum Mechanics (Nonrelativistic Theory) (Pergamon Press, New York, 1977)

    Google Scholar 

  26. E. Schrödinger, Die gegenwartige Situation in der Quanenmechanik. Naturwissenschaften 23, S. 807–812, 823–843, 844–849 (1935)

    Google Scholar 

  27. E. Schrödinger, The present situation in quantum mechanics, in Quantum Theory and Measurement, ed. by J.A. Wheeler, W.H. Zurek (Princeton University Press, Princeton, 1983), pp. 152–168

    Google Scholar 

  28. R. Landauer, The physical nature of information. Phys. Lett. A217, 188–193 (1996)

    MathSciNet  ADS  Google Scholar 

  29. R. Landauer, Minimal energy requirements in communication. Science 272, 1914–1918 (1996)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  30. L. Szilard, Über die Entropieverminderung in einen thermodynamischen System bei Eingriffen intelligenter Wesen. Zs. Phys. 53, 840 (1929)

    Article  ADS  MATH  Google Scholar 

  31. L. Szilard, On the decrease of entropy in a thermodynamic system by the intervention of intelligent beings, in Quantum Theory and Measurement, ed. by J.A. Wheeler, W.H. Zurek (Princeton University Press, Princeton, 1983), pp. 539–549

    Google Scholar 

  32. C.M. Caves, W.G. Unruh, W.H. Zurek, Comment on quantitative limits on the ability of a Maxwell demon to extract work from heat. Phys. Rev. Lett. 65, 1387–1390 (1990)

    Article  ADS  Google Scholar 

  33. W.H. Zurek, Maxwell’s demon. Szillard’s engine and quantum measurement, ArXiv: quant - ph/0301076

    Google Scholar 

  34. N.D. Mermin, Quantum Computer Science (Cambridge University Press, Cambridge, 2007)

    MATH  Google Scholar 

  35. D. McMahon, Quantum Computing Explained (Wiley Interscience, Hoboken, NJ, 2008)

    MATH  Google Scholar 

  36. R. Landauer, Irreversibility and heat generation in the computation proces. IBM J. Res. Develop. 3, 183–204 (1961)

    Article  MathSciNet  Google Scholar 

  37. C. Bennett, The thermodynamics of computation. Int. J. Theor. Phys. 21, 905–940 (1982)

    Article  Google Scholar 

  38. C. Bennett, Quantum information: qubits and quantum error correction. Int. J. Theor. Phys. 42, 153–176 (2003)

    Article  MATH  Google Scholar 

  39. A. Barenco, Quantum physics and computers. Contemporary Phys. 37, 375–389 (1996)

    Google Scholar 

  40. A. Barenco, Quantum computation: an introduction, in [173] pp. 143–184

    Google Scholar 

  41. C. Bennett, Quantum information and computation. Phys. Today 48, 24–30 (1995)

    Article  Google Scholar 

  42. D. Deutsch, Quantum theory, the Church-Turing principle and the universal quantum computer. Proc. Roy. Soc. (London) 400, 97–117 (1985)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  43. D. Deutsch, The Fabric of Reality (Penguin Press, Allen Line, 1998)

    Google Scholar 

  44. S. Ya, Kilin. Quantum information. Phys. - Uspekhi 42, 435–456 (1999)

    Google Scholar 

  45. W.K. Wooters, W.H. Zurek, A single quantum state cannot be cloned. Nature 299, 802–803 (1982)

    Article  ADS  Google Scholar 

  46. D. Dieks, Communications by EPR - devices. Phys. Lett. A92, 271–272 (1982)

    ADS  Google Scholar 

  47. B. Schumacher, Quantum coding. Phys. Rev. A51, 2738–2747 (1995)

    MathSciNet  ADS  Google Scholar 

  48. R. Josza, Quantum information and its properties, in [51], pp. 49–75

    Google Scholar 

  49. T. Spiller, Quantum information processing: cryptography, computation, and teleportation. Proc. IEEE 84, 1719–1746 (1996)

    Article  Google Scholar 

  50. T. Spiller, Basic elements of quantum information technology, in [51], pp. 1–28

    Google Scholar 

  51. H.-K. Lo, T. Spiller, S. Popescu (eds.), Introduction to Quantum Computation and Quantum Information (World Scientific, London, 1998)

    Google Scholar 

  52. D. Bouwmesater, A.K. Ekert, A. Zeilinger (eds.), The Physics of Quantum Information: Quantum Cryptography, Teleportation, Computation (Springer, New York, 2000)

    Google Scholar 

  53. YuI Manin, Countable and Uncountable (Soviet Radio, Moscow, 1980). (in Russian)

    Google Scholar 

  54. P. Benioff, The computer as a physical system: A microscopic quantum mechanical Hamiltonian model of computers as represented by Turing machine. J. Stat. Phys. 22, 563–591 (1980)

    Article  MathSciNet  ADS  Google Scholar 

  55. P. Benioff, Quantum mechanical Hamiltonian models of Turing machine. J. Stat. Phys. 29, 515–546 (1982)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  56. P. Benioff, Quantum mechanical models of Turing machines that dissipate no energy. Phys. Rev. Lett. 48, 1681–1684 (1982)

    Article  MathSciNet  ADS  Google Scholar 

  57. R. Feinman, Quantum computers. Found. Phys. 16, 507–532 (1986)

    Article  MathSciNet  ADS  Google Scholar 

  58. A. Einstein, B. Podolsky, B.N. Rosen, Can quantum mechanical description of physical reality considered complete? Phys. Rev. 47, 777–780 (1935)

    Article  ADS  MATH  Google Scholar 

  59. J.S. Bell, Speakable and Unspeakable in Quantum Mechanics (Cambridge University Press, Cambridge, 1987)

    MATH  Google Scholar 

  60. D.P. DiVincenzo, Physical implementation of quantum computation. Fortsch. Physik (Prog. Phys.) 48, 771–780 (2000); ArXiv: quant - ph/0002077

    Google Scholar 

  61. P.W. Shor, Polynomial - time algorithms for prime factorization and discrete logarithms on a quantum computers. SIAM J. Comput. 26, 1494–1509 (1997); ArXiv: quant - ph/ 9508027

    Google Scholar 

  62. P.W. Shor, Introduction to quantum algorithm. AMS PSARM 58, 143–159 (2002); ArXiv, quant - ph/ 0005003

    Google Scholar 

  63. J. Eisert, M.M. Wolf, Quantum computing. in Handbook Innovative Computing (Springer, Berlin, Heidelberg, 2004)

    Google Scholar 

  64. L.K. Grover, Quantum mechanics helps in searching for a needle a haytack. Phys. Rev. Lett. 79, 325–328 (1997)

    Article  ADS  Google Scholar 

  65. L.K. Grover, Tradeoffs in the quantum search algorithm. ArXiv, quant - ph/ 0201152

    Google Scholar 

  66. N. Yanofsky, M. Manucci, Quantum Computing for Computer Scientists (Camdridge University Press, Cambridge, 2008)

    Book  MATH  Google Scholar 

  67. J.F. Clauser, A. Shimony, Bell’s theorem: experimental tests and implications. Rep. Prog. Phys. 41, 1881–1927 (1978)

    Article  ADS  Google Scholar 

  68. D.M. Greenberger, M.A. Horne, A. Shimony, A. Zeilinger, Am. J. Phys. 58, 1131–1139 (1990)

    Article  MathSciNet  ADS  Google Scholar 

  69. A. Olaya-Castro, N.F. Johnson, Quantum information processing in nanostructures, ArXiv:quant - ph/0406133

    Google Scholar 

  70. C.H. Bennett, G. Brassard, C. Crepeau et al., Teleporting an unknown quantum state. Phys. Rev. Lett. 70, 1895–1899 (1995)

    Article  MathSciNet  ADS  Google Scholar 

  71. I.V. Bagratin, B.A. Grishanin, N.V. Zadkov, Entanglement quantum states of atomic systems. Phys. Uspekhi (Moscow) 171, 625–648 (2001). (in Russian)

    Google Scholar 

  72. A. Galindo, M.A. Martin-Delgado, Information and computation: classical and quantum aspects. Rev. Mod. Phys. 74, 347–423 (2002)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  73. D. Gammon, D.G. Steel, Optical studies of single quantum dots. Phys. Today (October 2002), pp. 36–41

    Google Scholar 

  74. M. Scheiber, A.S. Bracker, D.D. Gammon, Essential concepts in the optical properties of quantum dot molecules. Solid State Commun. 149, 1427–1435 (2009)

    Article  ADS  Google Scholar 

  75. S. Kiravittaya, A. Rastelli, O.G. Schmidt, Advanced quantum dot configurations. Rep. Prog. Phys. 72, 046502–34 (2009)

    Article  ADS  Google Scholar 

  76. V.M. Agranovich, D.M. Galanin, Transfer the Energy of the Electronic Excitation in Condensed Matter (Science, Moscow, 1978). (in Russian)

    Google Scholar 

  77. V.G. Plekhanov, Elementary excitations in isotope-mixed crystals. Phys. Rep. 410, 1–235 (2005)

    Article  ADS  Google Scholar 

  78. S. Singh, The Code Book: The Science of Secrecy from Ancient Egypt to Quantum Cryptography (Fourth Estate, London, 1999)

    Google Scholar 

  79. W. Diffie, M.E. Hellman, Privacy and authentication: an introduction to cryptography. IEEE Trans. Inf. Theory 67, 71–109 (1976)

    MathSciNet  Google Scholar 

  80. G. Gilbert, M. Hamric, Practical Quantum Cryptography: A Comprehensive Analysis, ArXiv: quant - ph/0009027; 0106043

    Google Scholar 

  81. D. Mayers, Unconditional security in quantum cryptography, Arxiv quant - ph/0003004

    Google Scholar 

  82. E. Wolf, Quantum cryptography. in Progress in Optics, vol 49 (Elsevier, Amsterdam, 2006)

    Google Scholar 

  83. N. Gisin, G. Ribordy, W. Tittel, H. Zbinden, Quantum cryptography. Rev. Mod. Phys. 74, 145–195 (2002)

    Article  ADS  Google Scholar 

  84. H.-K. Lo, Quantum cryptology, in [51] pp. 76–119

    Google Scholar 

  85. See the articles in the issue IEEE 76 (1988)

    Google Scholar 

  86. S. Wiesner, Conjugate coding. SIGAST News 15, 78–88 (1983)

    Google Scholar 

  87. M.O. Rabin, How to exchange secrets by oblivious transfer. Techn. Memo, TR - 81 (Aiken Computation Laboratory, Harvard University, 1981)

    Google Scholar 

  88. C.H. Bennett, G. Brassard, C. Crepeau, Practical quantum oblivious tranfer. Advances in Cryptology, Crypto’91, Lecture Notes in Computer Science, vol 576, (Springer-Verlag, Berlin, 1992), pp. 351–366

    Google Scholar 

  89. C.H. Bennett, G. Brassard, Quantum cryptography. in Proceedings of IEEE International Conference on Computers, Systems, and Signal Processing (Bangalore, India, 1984), pp. 175–179

    Google Scholar 

  90. C.H. Bennet, F. Bessette, G. Brassard et al., Experimental quantum cryptography. J. Cryptology 5, 3–28 (1992)

    Article  Google Scholar 

  91. A.K. Ekert, Quantum cryptography based on Bell’s theorem. Phys. Rev. Letters 67, 661–665 (1991)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  92. A. Ekert, R. Jozsa, Quantum computation and Shor’s factoring algorithm. Rev. Mod. Phys. 68, 733–753 (1996)

    Article  MathSciNet  ADS  Google Scholar 

  93. H. Zbinden, Experimental quantum cryptography, in [51] pp. 120–143

    Google Scholar 

  94. R. Renner, Security quantum key distribution. Ph.D. of Natural Science (Swiss Federal Institute of Technology, Zurich, 2005)

    Google Scholar 

  95. D. Stucki, N. Gisin, O. Guinnard, R. Ribordy, H. Zbinden, Quantum key distribution over 67 km a plug&play system. New J. Phys. 4, 41–8 (2002)

    Article  ADS  Google Scholar 

  96. C.H. Bennett, Quantum cryptography using any two nonorthogonal states. Phys. Rev. Let. 68, 3121–3124 (1992)

    Article  ADS  MATH  Google Scholar 

  97. C.H. Bennett, G. Brassard, N.D. Mermin, Quantum cryptography without Bell’s theorem. Phys. Rev. Letters 68, 557–559 (1992)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  98. R.J. Hughes, D.M. Adle, P. Duer et al., Quantum cryptography. Contemp. Phys. 36, 149–163 (1995)

    Article  ADS  Google Scholar 

  99. K. Goser, P. Glösekötter, J. Dienstuhl, Nanoelectronics and Nanosystems (Springer, Berlin, 2004)

    Google Scholar 

  100. T.A. Walker, Relationships between Quantum and Classical Information, Ph. D. Thesis (University of York, 2008)

    Google Scholar 

  101. S.L. Braunstein, Quantum Computations (Encyclopedia of Applied Physics, Wiley - VCH, New York, 1999), pp. 239–256

    Book  Google Scholar 

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  1. Mathematics and Physics Department, Computer Science College, Erika Street 7a, 10416, Tallinn, Estonia

    Vladimir G. Plekhanov

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Plekhanov, V.G. (2012). Classical and Quantum Information. In: Isotope-Based Quantum Information. SpringerBriefs in Physics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-28750-3_3

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