Not-so-normal mode decomposition

Physical Review Letters

Volumn 100, Issue 7, 2008, Pages

  Wolf, Michael M ^a  

^a MAX PLANCK INSTITUT FÜR QUANTENOPTIK   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

CONSTRAINT THEORY; OSCILLATORS (ELECTRONIC);

CANONICAL MATRIX; MULTIMODE CHANNELS; NORMAL MODE DECOMPOSITION; SYMPLECTIC EQUIVALENCE TRANSFORMATIONS;

MATHEMATICAL TRANSFORMATIONS;

EID: 40849088473     PISSN: 00319007     EISSN: 10797114     Source Type: Journal    
DOI: 10.1103/PhysRevLett.100.070505     Document Type: Article

References (29)

1. J. Williamson, Am. J. Math. 58, 141 (1936); AJMAAN 0002-9327 10.2307/2371062
2. J. Williamson Am. J. Math. 59, 599 (1937); AJMAAN 0002-9327 10.2307/2371583
3. J. Williamson Am. J. Math. 61, 897 (1939). AJMAAN 0002-9327 10.2307/2371633
4. W.C. Waterhouse, Linear Algebra Appl. 396, 385 (2005); LAAPAW 0024-3795 10.1016/j.laa.2004.10.003
5. H. Fassbender, D.S. Mackey, N. Mackey, and H. Xu, Linear Algebra Appl. 287, 125 (1999). LAAPAW 0024-3795 10.1016/S0024-3795(98)10137-4
6. Kh.D. Ikramov and E.A. Zaikova, Vestnik Moskov. Univ. Ser. XV Vychisl. Mat. Kibernet. 1, 23 (1988).
7. B. Arvind, N. Dutta, R. Mukunda, and P. Simon, Pramana PRAMCI 0304-4289 45, 471 (1995).
8. S.L. Braunstein and P. van Loock, Rev. Mod. Phys. 77, 513 (2005). RMPHAT 0034-6861 10.1103/RevModPhys.77.513
9. H.Y. Ling, H. Pu, and B. Seaman, Phys. Rev. Lett. 93, 250403 (2004). PRLTAO 0031-9007 10.1103/PhysRevLett.93.250403
10. K.D. Kokkotas and B.G. Schmidt, Living Rev. Relativity 1433-8351 2, 2 (1999).
11. L.J. Garay, J.R. Anglin, J.I. Cirac, and P. Zoller, Phys. Rev. Lett. 85, 4643 (2000). PRLTAO 0031-9007 10.1103/PhysRevLett.85.4643
12. G. Frobenius, Sitzungsber. Preuss. Akad. für Wiss. 3 (1910);
13. A.J. Bosch, Am. Math. Mon. AMMYAE 0002-9890 93, 462 (1986). 10.2307/2323471
14. R.A. Horn and C.R. Johnson, Matrix Analysis (Cambridge University Press, Cambridge, England, 1985).
15. A.J. Laub and K. Meyer, Celest. Mech. 9, 213 (1974); CLMCAV 0008-8714 10.1007/BF01260514
16. V.I. Arnold, Mathematical Methods of Classical Mechanics (Springer, New York, 1978).
17. K. Hammerer, E.S. Polzik, and J.I. Cirac, Phys. Rev. A 72, 052313 (2005). PLRAAN 1050-2947 10.1103/PhysRevA.72.052313
18. A. Botero and B. Reznik, Phys. Rev. A 67, 052311 (2003). PLRAAN 1050-2947 10.1103/PhysRevA.67.052311
19. A.S. Holevo and R.F. Werner, Phys. Rev. A 63, 032312 (2001). PLRAAN 1050-2947 10.1103/PhysRevA.63.032312
20. M. Navascues, J. Bae, J.I. Cirac, M. Lewestein, A. Sanpera, and A. Acin, Phys. Rev. Lett. 94, 010502 (2005). PRLTAO 0031-9007 10.1103/PhysRevLett.94. 010502
21. G. Giedke, J. Eisert, J.I. Cirac, and M.B. Plenio, Quantum Inf. Comput. QICUAW 1533-7146 3, 211 (2003).
22. J. Fiurasek and L. Mista, Phys. Rev. A 75, 060302(R) (2007). PLRAAN 1050-2947 10.1103/PhysRevA.75.060302
23. G. Adesso, Phys. Rev. Lett. 97, 130502 (2006). PRLTAO 0031-9007 10.1103/PhysRevLett.97.130502
24. J. Eisert and M.M. Wolf, in Quantum Information with Continuous Variables, edited by, G. Leuchs, N. Cerf, and, E. Polzik, (Imperial College Press, London, 2005).
25. B. Julsgaard, J. Sherson, J.I. Cirac, Jaromir Fiurasek, and E.S. Polzik, Nature (London) NATUAS 0028-0836 432, 482 (2004). 10.1038/nature03064
26. A. Serafini, J. Eisert, and M.M. Wolf, Phys. Rev. A 71, 012320 (2005); PLRAAN 1050-2947 10.1103/PhysRevA.71.012320
27. M.M. Wolf, D. Perez-Garcia, and G. Giedke, Phys. Rev. Lett. 98, 130501 (2007); PRLTAO 0031-9007 10.1103/PhysRevLett.98.130501
28. F. Caruso, V. Giovannetti, and A.S. Holevo, New J. Phys. 8, 310 (2006). NJOPFM 1367-2630 10.1088/1367-2630/8/12/310
29. A.S. Holevo, Probl. Inf. Transm. PRITA9 0032-9460 43, 1 (2007). 10.1134/S0032946007010012