Why two qubits are special

Journal of Mathematical Physics

Volumn 41, Issue 10, 2000, Pages 6772-6782

  Vollbrecht, K G H ^a   Werner, R F ^a  

^a TECHNICAL UNIVERSITY OF BRAUNSCHWEIG   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0034345339     PISSN: 00222488     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.1286032     Document Type: Article

References (21)

1. R. P. Feynman, R. B. Leighton, and M. Sands, The Feynman Lectures on Physics (Addison-Wesley, Reading, 1966), Vol. III.
2. C. H. Bennet, G. Brassard, C. Crepeau, R. Joza, A. Peres, and W. K. Wootters, "Teleporting an unknown quantum state via dual classical and Einstein-Podolsky-Rosen channels." Phys. Rev. Lett. 70, 1895-1899 (1993).
3. C. H. Bennett and S. J. Wiesner, "Communication via one-and two-particle operators on Einstein-Podolsky-Rosen states," Phys. Rev. Lett. 69, 2881-2884 (1992).
4. M. Horodecki, P. Horodecki, and H. Horodecki, "Separability of mixed states: Necessary and sufficient conditions," Phys. Lett. A 233, 1-8 (1996).
5. W. K. Wootters, "Entanglement of formation of an arbitrary state of two qubits," Phys. Rev. Lett. 80, 2245-2248 (1998).
6. S. Hill and W. K. Wootters, "Entanglement of a pair of quantum bits," Phys. Rev. Lett. 78, 5022-5025 (1997).
7. C. H. Bennett, D. P. DiVincenzo, J. A. Smolin, and W. K. Wootters, "Mixed state entanglement and quantum error correction," Phys. Rev. A 54, 3824-3851 (1996).
8. G. G. Emch, Algebraic methods in Statistical Mechanics and Quantum Field Theory (Wiley, New York, 1972).
9. A. M. Gleason, "Measures on the closed subspaces of a Hilbert space," J. Math. Mech. 6, 885-893 (1957).
10. R. Cooke, M. Keane, and W. Moran, "An elementary proof of Gleason's theorem," Math. Proc. Cambridge Philos. Soc. 98, 117 (1985).
11. V. Bužek, M. Hillery, and R. F. Werner, "Optimal manipulation with qubits: Universal NOT gate," Phys. Rev. A 60, R2626-R2629 (1999).
12. A. Eckert and P. L. Knight, "Entangled quantum systems and the Schmidt decomposition," Am. J. Phys. 63, 415-423 (1995).
13. 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, 1895-1899 (1993).
14. J. Denes and A. D. Keedwell. Latin Squares and Their Applications (English Universities Press, London, 1977).
15. S. S. Agaian, Hadamard Matrices and Applications (Springer Lecture Notes in Mathematics, Springer-Verlag, Berlin, 1985).
16. J. Wallis, Complex Hadamard matrices, Lin.multilin.Algebra 1 (1973) 257-272.
17. F. J. MacWilliams and N. J. A. Sloane, The Theory of Error-Correcting Codes I,II (North-Holland, Amsterdam, 1977).
18. E. P. Wigner, Gruppentheorie und ihre Anwendung auf Quantenmechanik der Atomspektren (Vieweg, Braunschweig, 1931).
19. R. V. Kadison, "Isometries of operator algebras," Ann. Math. 54, 325-338 (1951).
20. E. B. Davies, Quantum Theory of Open Systems (Academic, New York, 1976).
21. P. E. T. Jørgensen and R. F. Werner, "Coherent states of the q-canonical commutation relations," Commun. Math. Phys. 164, 455-471 (1994).