Abstract
We turn now to the description of the building blocks of quantum information theory. We introduce the quantum analog of the bit—qubit, single- and multiple-qubit logic gates and quantum circuits performing information processing. Any introduction to quantum information theory would be incomplete if it did not contain a discussion on the peculiar properties of the entanglement, which results, on the one hand, in the notorious non-locality of quantum mechanics, and on the other hand, in decoherence already studied in previous chapters in the general framework of a small quantum system coupled to a large reservoir. A significant part of this chapter is therefore devoted to the analysis of the role of entanglement in the fundamental tests of quantum mechanics, as well as its quantum information applications such as cryptography, teleportation and dense coding.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Chapter 8
V. Scarani, S. Iblisdir, N. Gisin and A. Acin, Quantum cloning, Rev. Mod. Phys. 77, 1225 (2005).
M. O. Scully, B. G. Englert and H. Walther, Quantum optical tests of complementarity, Nature 351 111 (1991).
A. Einstein, B. Podolsky and N. Rosen, Can quantum-mechanical description of physical reality be considered complete?, Phys. Rev. 47, 777 (1935)
N. Bohr, Can quantum-mechanical description of physical reality be considered complete?, Phys. Rev. 48, 696 (1935).
J. S. Bell, On the Einstein Podolsky Rosen paradox, Physics 1, 195 (1964); J. S. Bell, On the problem of hidden variables in quantum mechanics, Rev. Mod. Phys. 38, 447 (1966).
J. F. Clauser, M. A. Horne, A. Shimony and R.A. Holt, Proposed experiment to test local hidden-variable theories, Phys. Rev. Lett. 23, 880 (1969); J. F. Clauser and M. A. Horne, Experimental consequences of objective local theories, Phys. Rev. D 10, 526 (1974).
A. Aspect, P. Grangier and G. Roger, Experimental realization of Einstein-Podolsky-Rosen-Bohm Gedankenexperiment: A new violation of Bell’s inequalities, Phys. Rev. Lett. 49, 91 (1982).
A. Zeilinger, Experiment and the foundations of quantum physics, Rev. Mod. Phys. 71, S288 (1999); R.Werner and M. Wolf, Bell inequalities and entanglement, Quant. Inf. Comput. 1(3) 1, (2001).
D. M. Greenberger, M. Horne and A. Zeilinger, in Bell’s Theorem, Quantum Theory, and Conceptions of the Universe, edited by M. Katafos (Kluwer Academic, 1988), p 73; D. M. Greenberger, M. A. Horne, A. Shimony and A. Zeilinger, Bell’s theorem without inequalities, Am. J. Phys. 58, 1131 (1990).
C. H. Bennett, G. Brassard, C. Crepeau, R. Jozsa, A. Peres and W. K. Wootters, Teleporting an unknown quantum state via dual classical and Einstein-Podolsky-Rosen channels, Phys. Rev. Lett. 70, 1895 (1993).
C. H. Bennett and S. J. Wiesner, Communication via one-and two-particle operators on Einstein-Podolsky-Rosen states, Phys. Rev. Lett. 69, 2881 (1992).
C. H. Bennett, G. Brassard, S. Popescu, B. Schumacher, J. A. Smolin and W. K. Wootters, Purification of noisy entanglement and faithful teleportation via noisy channels, Phys. Rev. Lett. 76, 722 (1996).
C. H. Bennett and G. Brassard, in Proceedings of IEEE International Conference on Computers, Systems, and Signal Processing, Bangalore, India, (IEEE, 1984) p. 175; C. H. Bennett, Quantum cryptography using any two nonorthogonal states, Phys. Rev. Lett. 68, 3121 (1992); A. K. Ekert, Quantum cryptography based on Bell’s theorem, Phys. Rev. Lett. 67, 661 (1991); C. H. Bennett, G. Brassard and N. D. Mermin, Quantum cryptography without Bell’s theorem, Phys. Rev. Lett. 68, 557 (1992).
N. Gisin, G. Ribordy, W. Tittel and H. Zbinden, Quantum cryptography, Rev. Mod. Phys. 74, 145 (2002).
D. C. H. Bennett and D. P. DiVincenzo, Quantum information and computation, Nature 404, 247 (2000).
A. Galindo and M. A. Martin-Delagado, Information and computation: Classical and quantum aspects, Rev. Mod. Phys. 74, 347 (2002).
C. E. Shannon, A mathematical theory of communication, Bell Syst. Thech. J. 27, 379 (1948); 27, 623 (1948); 28, 656 (1949).
B. Schumacher, Quantum coding, Phys. Rev. A 51, 2738 (1995).
C. H. Bennett, D. P. DiVincenzo, J. A. Smolin and W. K. Wootters, Mixed-state entanglement and quantum error correction, Phys. Rev. A 54, 3824 (1996).
W. K. Wootters, Entanglement of formation of an arbitrary state of two qubits, Phys. Rev. Lett. 80, 2245 (1998); P. Rungta, V. Bužek, C. M. Caves, M. Hillery and G. J. Milburn, Universal state inversion and concurrence in arbitrary dimensions, Phys. Rev. A 64, 042315 (2001).
Rights and permissions
Copyright information
© 2007 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
(2007). Fundamentals of Quantum Information. In: Fundamentals of Quantum Optics and Quantum Information. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-34572-5_8
Download citation
DOI: https://doi.org/10.1007/978-3-540-34572-5_8
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-34571-8
Online ISBN: 978-3-540-34572-5
eBook Packages: Physics and AstronomyPhysics and Astronomy (R0)