Linear optics and quantum maps

Physical Review A - Atomic, Molecular, and Optical Physics

Volumn 76, Issue 3, 2007, Pages

  Aiello, A ^a   Puentes, G ^a   Woerdman, J P ^a  

^a LEIDEN UNIVERSITY   (Netherlands)

Author keywords

[No Author keywords available]

Indexed keywords

LIGHT POLARIZATION; PHOTONS; QUANTUM THEORY;

LINEAR OPTICS; POLARIZATION OPTICS; QUANTUM FORMALISM; STOKES-JONES-MUELLER DESCRIPTION;

QUANTUM OPTICS;

EID: 34748831030     PISSN: 10502947     EISSN: 10941622     Source Type: Journal    
DOI: 10.1103/PhysRevA.76.032323     Document Type: Article

References (48)

1. M. A. Nielsen and I. L. Chuang, Quantum Computation and Quantum Information, reprinted 1st ed. (Cambridge University Press, Cambridge, UK, 2002)
2. A. Zeilinger, Rev. Mod. Phys. RMPHAT 0034-6861 10.1103/RevModPhys.71.S288 71, S288 (1999).
3. N. Gisin, G. Ribody, W. Tittel, and H. Zbinden, Rev. Mod. Phys. RMPHAT 0034-6861 10.1103/RevModPhys.74.145 74, 145 (2002).
4. E. Knill, R. Laflamme, and G. Milburn, Nature (London) NATUAS 0028-0836 10.1038/35051009 409, 46 (2001).
5. J. L. O'Brien, G. J. Pryde, A. G. White, T. C. Ralph, and D. Branning, Nature (London) NATUAS 0028-0836 10.1038/nature02054 426, 264 (2003).
6. J. Skaar, J. C. G. Escartín, and H. Landro, Am. J. Phys. AJPIAS 0002-9505 10.1119/1.1775241 72, 1385 (2004).
7. P. Kok, W. J. Munro, K. Nemoto, T. C. Ralph, J. P. Dowling, and G. J. Miburn, Rev. Mod. Phys. RMPHAT 0034-6861 10.1103/RevModPhys.79.135 79, 135 (2007), and references therein.
8. D. Bouwmeester, J. W. Pan, K. Mattle, M. Eibl, H. Weinfurter, and A. Zeilinger, Nature (London) NATUAS 0028-0836 10.1038/37539 390, 575 (1997).
9. D. Boschi, S. Branca, F. De Martini, L. Hardy, and S. Popescu, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.80.1121 80, 1121 (1998).
10. D. F. V. James, P. G. Kwiat, W. J. Munro, and A. G. White, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.64.052312 64, 052312 (2001).
11. J. L. O'Brien, G. J. Pryde, A. Gilchrist, D. F. V. James, N. K. Langford, T. C. Ralph, and A. G. White, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.93.080502 93, 080502 (2004).
12. N. Peters, J. Altepeter, E. Jeffrey, D. A. Branning, and P. Kwiat, Quantum Inf. Comput. 3, 503 (2003). 0890-5401
13. T.-C. Wei, J. B. Altepeter, D. Branning, P. M. Goldbart, D. F. V. James, E. Jeffrey, P. G. Kwiat, S. Mukhopadhyay, and N. A. Peters, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.71.032329 71, 032329 (2005).
14. A. Yariv, Quantum Electronics, 3rd ed. (Wiley, New York, 1989).
15. C. Zhang, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.69.014304 69, 014304 (2004).
16. N. Brunner, A. Acín, D. Collins, N. Gisin, and V. Scarani, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.91.180402 91, 180402 (2003).
17. A. Aiello, G. Puentes, D. Voigt, and J. P. Woerdman, Opt. Lett. OPLEDP 0146-9592 10.1038/nature04440 31, 817 (2006).
18. M. Born and E. Wolf, Principles of Optics, 7th ed. (Cambridge University Press, Cambridge, 1999).
19. J. N. Damask, Polarization Optics in Telecommunications (Springer, New York, 2005).
20. U. Leonhardt, Rep. Prog. Phys. RPPHAG 0034-4885 10.1088/0034-4885/66/7/ 203 66, 1207 (2003).
21. G. Puentes, D. Voigt, A. Aiello, and J. P. Woerdman, e-print arXiv:quant-ph/0607014.
22. D. L. Falkoff and J. E. McDonald, J. Opt. Soc. Am. 41, 862 (1951) 0030-3941
23. U. Fano, Phys. Rev. PHRVAO 0031-899X 10.1103/PhysRev.93.121 93, 121 (1954).
24. J. J. Sakurai, Modern Quantum Mechanics (Benjamin/Cummings, Menlo Park, California, 1985).
25. Actually, our Stokes parameters sα differ from the traditional ones Sα as given, e.g., in Chap. 10 of. However, the two sets of parameters are related by the simple relations S0 = s0, S1 = s3, S2 = s1, S3 =- s2.
26. F. Le Roy-Brehonnet and B. L. Jeune, Prog. Quantum Electron. PQUEAH 0079-6727 10.1016/S0079-6727(97)84687-3 21, 109 (1997).
27. S.-Y. Lu and R. A. Chipman, J. Opt. Soc. Am. A 13, 1106 (1996). 0740-3232
28. A. Fujiwara and P. Algoet, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.59.3290 59, 3290 (1999).
29. A. Aiello and J. P. Woerdman, e-print arXiv:math-ph/0412061.
30. J. J. Gil, J. Opt. Soc. Am. A JOAOD6 0740-3232 10.1364/JOSAA.17.000328 17, 328 (2000).
31. K. Kim, L. Mandel, and E. Wolf, J. Opt. Soc. Am. A 4, 433 (1987). 0740-3232
32. M. B. Ruskai, S. Szarek, and E. Werner, Linear Algebr. Appl. LAAPAW 0024-3795 10.1016/S0024-3795(01)00547-X 347, 159 (2002).
33. D. G. M. Anderson and R. Barakat, J. Opt. Soc. Am. A 11, 2305 (1994). 0740-3232
34. R. Simon, Opt. Commun. OPCOB8 0030-4018 10.1016/0030-4018(82)90234-6 42, 293 (1982).
35. I. Bengtsson and K. Życzkowski, Geometry of Quantum States: An Introduction to Quantum Entanglement (Cambridge University Press, Cambridge, 2006).
36. E. C. G. Sudarshan, P. M. Mathews, and J. Rau, Phys. Rev. PHRVAO 0031-899X 10.1103/PhysRev.121.920 121, 920 (1961)
37. M.-D. Choi, Linear Algebra Appl. 10, 285 (1975).
38. S. R. Cloude, Optik (Stuttgart) OTIKAJ 0030-4026 75, 26 (1986)
39. S. R. Cloude, Proc. SPIE PSISDG 0277-786X 1166, 177 (1989)
40. S. R. Cloude, J. Electromagn. Waves Appl. 6, 947 (1992). 0920-5071
41. We acknowledge Dr. Krzysztof Wódkiewick, who pointed out to us the importance of this point.
42. A. Aiello and J. P. Woerdman, Opt. Lett. OPLEDP 0146-9592 10.1364/OL.30.001599 30, 1599 (2005).
43. M. Ziman and V. Buek, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.72. 052325 72, 052325 (2005).
44. A. Aiello, G. Puentes, D. Voigt, and J. P. Woerdman, e-print arXiv:quant-ph/0603182.
45. N. A. Peters, J. B. Altepeter, D. A. Branning, E. R. Jeffrey, T.-C. Wei, and P. G. Kwiat, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.92.133601 92, 133601 (2004).
46. R. F. Werner, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.40.4277 40, 4277 (1989).
47. J. Morio and F. Goudail, Opt. Lett. OPLEDP 0146-9592 10.1364/OL.29.002234 29, 2234 (2004).
48. M. Barbieri, F. De Martini, G. Di Nepi, and P. Mataloni, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.92.177901 92, 177901 (2004).