Schmidt information and entanglement of quantum systems

Moscow University Computational Mathematics and Cybernetics

Volumn 31, Issue 1, 2007, Pages 33-42

  Bogdanov, A Yu ^a   Bogdanov, Yu I ^a   Valiev, K A ^a  

^a MOSCOW STATE UNIVERSITY   (Russian Federation)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 45549102868     PISSN: 02786419     EISSN: 19348428     Source Type: Journal    
DOI: 10.3103/S0278641907010074     Document Type: Article

References (15)

1. K. A. Valiev and A. A. Kokin, Quantum Computers: Expectations and Reality (Regulyarnaya i Khaoticheskaya Dinamika, Moscow, Izhevsk, 2004).
2. A. Einstein, B. Podolsky, and N. Rosen, "Can Quantum Mechanical Description of Physical Reality be Considered Complete?," Phys. Rev. 47, 777-780 (1935).
3. N. Bohr, "Discussion with Einstein on Epistemology Problems in Atomic Physics," in Albert Einstein: Philosopher-Scientist, Ed. by P. A. Schilpp (Library of Living Philosophers, Evanston, Ill., 1949), pp. 200-241.
4. R. Feynman, "Simulating Physics with Computers," Int. J. Theor. Phys. 21, 467-488 (1982).
5. E. Schmidt, "Zur theorie der linearen und nicht linearen integralgleichungen," Math. Ann. 63, 433 (1906).
6. J. H. Eberly, "Schmidt Analysis of Pure-State Entanglement," lanl e-print arXiv: quant-ph/0508019.
7. K. W. Chan, C. K. Law, and J. H. Eberly, "Localized Single-Photon Wave Function in Free Space," Phys. Rev. Lett. 88, 100402 (2002).
8. C. K. Law, I. A. Walmsey, and J. H. Eberly, "Continuous Frequency Entanglement: Effective Finite Hilbert Space and Entropy Control," Phys. Rev. Lett. 84, 5304-5307 (2000).
9. L. Lamata and J. Leon, "Dealing with Entanglement of Continuous Variables: Schmidt Decomposition with Discrete Sets of Orthogonal Functions," lanl e-print arXiv: quant-ph/0410167 (2004).
10. A. Yu. Bogdanov, Yu. I. Bogdanov, and K. A. Valiev, "Schmidt Modes and Entanglement in Continuous-Variable Quantum Systems," Mikroelektronika 35(1), 11-30 (2006) [Russ. Microelectron. 35, 7 (2006)].
11. Probability and Mathematical Statistics: Encyclopedia, Ed. by Yu. V. Prokhorov (Bolshaya Rossiiskaya Entsiklopediya, Moscow, 1999).
12. L. D. Landau and E. M. Lifshits, Statistical Physics (Nauka, Moscow, 1995; Pergamon, Oxford, 1980), Part 1.
13. S. Popescu, A. J. Short, and A. Winter, "Entanglement and the Foundations of Statistical Mechanics," lanl e-print arXiv: quant-ph/0511225 (2005).
14. C. Cohen-Tannoudji, B. Diu, and F. Laloé, Mecanique quantique (Hermann, Paris, 1973; Izd. Ural Univ., Yekaterinburg, 2000).
15. N. Ya. Vilenkin, Special Functions and the Theory of Group Representation (Nauka, Moscow, 1991; Am. Math. Soc., Providence, R. I., 1968).