Extremality of Gaussian quantum states

Physical Review Letters

Volumn 96, Issue 8, 2006, Pages

  Wolf, Michael M ^a   Giedke, Geza ^a,b   Cirac, J Ignacio ^a  

^a MAX PLANCK INSTITUT FÜR QUANTENOPTIK   (Germany)

^b ETH ZURICH   (Switzerland)

Author keywords

[No Author keywords available]

Indexed keywords

BOSONIC QUANTUM CHANNELS; COVARIANCE MATRIX; GAUSSIAN APPROXIMATIONS; GAUSSIAN QUANTUM STATES;

APPROXIMATION THEORY; MATRIX ALGEBRA; OPTIMAL SYSTEMS;

QUANTUM THEORY;

EID: 33644639117     PISSN: 00319007     EISSN: 10797114     Source Type: Journal    
DOI: 10.1103/PhysRevLett.96.080502     Document Type: Article

References (33)

1. A.S. Holevo, M. Sohma, and O. Hirota, Phys. Rev. A 59, 1820 (1999). PLRAAN 1050-2947 10.1103/PhysRevA.59.1820
2. A.S. Holevo and R.F. Werner, Phys. Rev. A 63, 032312 (2001). PLRAAN 1050-2947 10.1103/PhysRevA.63.032312
3. F. Grosshans and N.J. Cerf, Phys. Rev. Lett. 92, 047905 (2004). PRLTAO 0031-9007 10.1103/PhysRevLett.92.047905
4. J. Eisert and M.M. Wolf, quant-ph/0505151.
5. A.S. Holevo, Probabilistic and Statistical Aspects of Quantum Theory (North-Holland, Amsterdam, 1982).
6. J. Quaegebeur, J. Funct. Anal. 57, 1 (1984). JFUAAW 0022-1236 10.1016/0022-1236(84)90097-1
7. C.D. Cushen and R.L. Hudson, J. Appl. Probab. JPRBAM 0021-9002 8, 454 (1971).
8. G.F. Dell'Antonio, Commun. Pure Appl. Math. 20, 413 (1967); CPMAMV 0010-3640
9. E.B. Davies, Commun. Math. Phys. 15, 277 (1969); CMPHAY 0010-3616 10.1007/BF01645529
10. E.B. Davies, Commun. Math. Phys. 27, 309 (1972). CMPHAY 0010-3616 10.1007/BF01645518
11. P.A.P. Moran, An Introduction to Probability Theory (Claredon, Oxford, 1968).
12. M. Horodecki, Quantum Inf. Comput. QICUAW 1533-7146 1 No. 1, 3 (2001).
13. G. Vidal and R.F. Werner, Phys. Rev. A 65, 032314 (2002); PLRAAN 1050-2947 10.1103/PhysRevA.65.032314
14. M.B. Plenio, Phys. Rev. Lett. 95, 090503 (2005). PRLTAO 0031-9007 10.1103/PhysRevLett.95.090503
15. G. Vidal, quant-ph/0203107.
16. G. Giedke, L.-M. Duan, J.I. Cirac, and P. Zoller, Quantum Inf. Comput. QICUAW 1533-7146 1 No. 3, 79 (2001);
17. L.-M. Duan, G. Giedke, J.I. Cirac, and P. Zoller, Phys. Rev. Lett. 84, 4002 (2000); PRLTAO 0031-9007 10.1103/PhysRevLett.84.4002
18. R.F. Werner and M.M. Wolf, Phys. Rev. Lett. 86, 3658 (2001). PRLTAO 0031-9007 10.1103/PhysRevLett.86.3658
19. M.A. Nielsen, Phys. Rev. A 61, 064301 (2000). PLRAAN 1050-2947 10.1103/PhysRevA.61.064301
20. M.E. Shirokov, quant-ph/0411091.
21. P.W. Shor, Commun. Math. Phys. CMPHAY 0010-3616 246, 453 (2004); 10.1007/s00220-003-0981-7
22. K. Matsumoto, T. Shimono, and A. Winter, Commun. Math. Phys. 246, 427 (2004); CMPHAY 0010-3616 10.1007/s00220-003-0919-0
23. K.M.R. Audenaert and S.L. Braunstein, Commun. Math. Phys. 246, 443 (2004). CMPHAY 0010-3616 10.1007/s00220-003-0987-1
24. M.M. Wolf and J. Eisert, New J. Phys. 7, 93 (2005). NJOPFM 1367-2630 10.1088/1367-2630/7/1/093
25. M. Christandl and A. Winter, J. Math. Phys. (N.Y.) JMAPAQ 0022-2488 45, 829 (2004). 10.1063/1.1643788
26. R. Alicki and M. Fannes, quant-ph/0312081.
27. A similar example but with fixed EPR uncertainty was found by J. Eisert (private communication).
28. S.J.v. Enk and O. Hirota, Phys. Rev. A 71, 062322 (2005). PLRAAN 1050-2947 10.1103/PhysRevA.71.062322
29. G. Giedke, M.M. Wolf, O. Krueger, R.F. Werner, and J.I. Cirac, Phys. Rev. Lett. 91, 107901 (2003). PRLTAO 0031-9007 10.1103/PhysRevLett.91.107901
30. M.M. Wolf, G. Giedke, O. Krueger, R.F. Werner, and J.I. Cirac, Phys. Rev. A 69, 052320 (2004). PLRAAN 1050-2947 10.1103/PhysRevA.69.052320
31. R.L. Hudson, J. Appl. Probab. JPRBAM 0021-9002 10, 502 (1973).
32. N.J. Cerf, O. Krueger, P. Navez, R.F. Werner, and M.M. Wolf, Phys. Rev. Lett. 95, 070501 (2005); PRLTAO 0031-9007 10.1103/PhysRevLett.95.070501
33. K. Hammerer, M.M. Wolf, E.S. Polzik, and J.I. Cirac, Phys. Rev. Lett. 94, 150503 (2005). PRLTAO 0031-9007 10.1103/PhysRevLett.94.150503