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Quantum Information Theory Fundamentals

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Quantum Biological Information Theory
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Abstract

In this chapter, we provide the basic concepts of quantum information processing and quantum information theory. The following topics from quantum information processing will be covered: state vectors, operators, density operators, measurements, dynamics of a quantum system, superposition principle, quantum parallelism, no-cloning theorem, and entanglement. The following concepts from quantum information theory will be provided: Holevo information, accessible information, Holevo bound, Shannon entropy and von Neumann entropy, Schumacher’s noiseless quantum coding theorem, and Holevo–Schumacher–Westmoreland theorem.

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References

  1. Djordjevic IB (2012) Quantum information processing and quantum error correction: an engineering approach. Elsevier/Academic Press, Amsterdam

    Google Scholar 

  2. Helstrom CW (1976) Quantum detection and estimation theory. Academic, New York

    MATH  Google Scholar 

  3. Helstrom CW, Liu JWS, Gordon JP (1970) Quantum mechanical communication theory. Proc IEEE 58:1578–1598

    Article  MathSciNet  Google Scholar 

  4. Sakurai JJ (1994) Modern quantum mechanics. Addison-Wesley, Reading

    Google Scholar 

  5. Gaitan F (2008) Quantum error correction and fault tolerant quantum computing. CRC, Boca Raton

    Book  MATH  Google Scholar 

  6. Baym G (1990) Lectures on quantum mechanics. Westview Press, New York

    Google Scholar 

  7. McMahon D (2007) Quantum computing explained. Wiley, Hoboken

    Book  Google Scholar 

  8. McMahon D (2006) Quantum mechanics demystified. McGraw-Hill, New York

    Google Scholar 

  9. Neilsen MA, Chuang IL (2000) Quantum computation and quantum information. Cambridge University Press, Cambridge

    Google Scholar 

  10. Fleming S (2008) PHYS 570: quantum mechanics (Lecture notes). University of Arizona, Tucson

    Google Scholar 

  11. Dirac PAM (1958) Quantum mechanics, 4th edn. Oxford University Press, London

    MATH  Google Scholar 

  12. Peleg Y, Pnini R, Zaarur E (1998) Schaum’s outline of theory and problems of quantum mechanics. McGraw-Hill, New York

    Google Scholar 

  13. Fowles GR (1989) Introduction to modern optics. Dover, New York

    Google Scholar 

  14. Scully MO, Zubairy MS (1997) Quantum optics. Cambridge University Press, Cambridge

    Book  Google Scholar 

  15. Le Bellac M (2006) A short introduction to quantum information and quantum computation. Cambridge University Press, Cambridge

    Book  MATH  Google Scholar 

  16. Pinter CC (2010) A book of abstract algebra. Dover, New York

    MATH  Google Scholar 

  17. Griffiths D (1995) Introduction to quantum mechanics. Prentice-Hall, Englewood Cliffs

    MATH  Google Scholar 

  18. Zettilli N (2001) Quantum mechanics, concepts and applications. Wiley, New York

    Google Scholar 

  19. Von Neumann J (1955) Mathematical foundations of quantum mechanics. Princeton University Press, Princeton

    MATH  Google Scholar 

  20. Jauch JM (1968) Foundations of quantum mechanics. Addison-Wesley, Reading

    MATH  Google Scholar 

  21. Peres A (1995) Quantum theory: concepts and methods. Kluwer, Boston

    MATH  Google Scholar 

  22. Goswami A (1996) Quantum mechanics. McGraw-Hill, New York

    Google Scholar 

  23. Jammer M (1974) Philosophy of quantum mechanics. Wiley, New York

    Google Scholar 

  24. McWeeny R (2003) Quantum mechanics, principles and formalism. Dover, Mineola

    Google Scholar 

  25. Weyl H (1950) Theory of groups and quantum mechanics. Dover, New York

    Google Scholar 

  26. Liboff RL (1997) Introductory quantum mechanics. Addison-Wesley, Reading

    Google Scholar 

  27. Cover TM, Thomas JA (1991) Elements of information theory. Wiley, New York

    Book  MATH  Google Scholar 

  28. Ingels FM (1971) Information and coding theory. Intext Educational Publishers, Scranton

    MATH  Google Scholar 

  29. Cvijetic M, Djordjevic IB (2013) Advanced optical communications and networks. Artech House, Boston

    Google Scholar 

  30. Djordjevic IB, Ryan W, Vasic B (2010) Coding for optical channels. Springer, New York

    Book  Google Scholar 

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Djordjevic, I.B. (2016). Quantum Information Theory Fundamentals. In: Quantum Biological Information Theory. Springer, Cham. https://doi.org/10.1007/978-3-319-22816-7_2

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  • DOI: https://doi.org/10.1007/978-3-319-22816-7_2

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-22815-0

  • Online ISBN: 978-3-319-22816-7

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