Publication: Quantum-invariant processes in phase space
Loading...
Official URL
Full text at PDC
Publication Date
2004-11-29
Authors
Advisors (or tutors)
Editors
Journal Title
Journal ISSN
Volume Title
Publisher
American Physical Society
Citations
Exportar
Abstract
We show the formal equivalence between the phase-space representations of transformations and quantum states. We study invariant quantum input-output transformations in phase space and in Hilbert space. We show that all invariant processes are linear transformations while the converse is not true. Some relevant examples of application of these ideas are examined.
Description
©2004 The American Physical Society
UCM subjects
Unesco subjects
Keywords
Citation
[1] U. Leonhardt and H. Paul, Prog. Quantum Electron. 19, 89 (1995); U. Leonhardt, Measuring the Quantum State of Light (Cambridge University Press, Cambridge, England, 1997); D.-G. Welsch, W. Vogel, and T. Opatrný, in Progress in Optics, edited by E. Wolf (Elsevier Science, Amsterdam, 1999), Vol. 39.
[2] G. S. Agarwal and E. Wolf, Phys. Lett. 26A, 485 (1968); Phys. Rev. Lett. 21, 180 (1968); G. S. Agarwal, Phys. Rev. 177, 400 (1969); G. S. Agarwal and E. Wolf, Phys. Rev. D 2, 2161 (1970); 2, 2187 (1970); 2, 2206 (1970).
[3] C. H. Page, J. Appl. Phys. 23, 103 (1952); H. Margenau and R. N. Hill, Prog. Theor. Phys. 26, 722 (1961); C. L. Mehta, J. Math. Phys. 5, 677 (1964); L. Cohen, ibid. 7, 781 (1966); N. C. Dias and J. N. Prata, Phys. Lett. A 302, 261 (2002); R. Gase, T. Gase, and K. Blüthner, Opt. Lett. 20, 2045 (1995).
[4] K. E. Cahill and R. J. Glauber, Phys. Rev. 177, 1857 (1969); 177, 1882 (1969); J. Peøina, Coherence of Light (Reidel, Dordrecht, 1985).
[5] D. M. Kaplan and G. C. Summerfield, Phys. Rev. 187, 639 (1969); F. T. Arecchi, E. Courtens, R. Gilmore, and H. Thomas, Phys. Rev. A 6, 2211 (1972); N. Mukunda, Am. J. Phys. 47, 182 (1979); J. P. Bizarro, Phys. Rev. A 49, 3255 (1994); J. Vaccaro, ibid. 52, 3474 (1995); Opt. Commun. 113, 421 (1995); G. S. Agarwal, Phys. Rev. A 24, 2889 (1981); M. O. Scully, Phys. Rev. D 28, 2477 (1983); J. C. Várilly and J. M. Gracia-BondÃa, Ann. Phys. (N.Y.) 190, 107 (1989); A. Luis and L. L. Sánchez-Soto, Quantum Opt. 5, 33 (1993); G. Ramachandran, A. R. Usha-Devi, P. Devi, and S. Sirsi, Found. Phys. 26, 401 (1996); V. V. Dodonov and V. I. Man’ko, Phys. Lett. A 229, 335 (1997); C. Brif and A. Mann, Phys. Rev. A 59, 971 (1999); S. M. Chumakov, A. Frank, and K. B. Wolf, ibid. 60, 1817 (1999); S. M. Chumakov, A. B. Klimov, and K. B. Wolf, ibid. 61, 034101 (2000); V. P. Karassiov and A. V. Masalov, J. Opt. B: Quantum Semiclassical Opt. 4, S366 (2002).
[6] W. K. Wootters, Ann. Phys. (N.Y.) 176, 1 (1987); O. Cohendet, Ph. Combe, M. Sirugue, and M. Sirugue-Collin, J. Phys. A 21, 2875 (1988); D. Galetti, and A. F. R. Toledo Piza, Physica A 149, 267 (1988); J. A. Vaccaro and D. T. Pegg, Phys. Rev. A 41, 5156 (1990); A. Lukš and V. Peøinová, Quantum Opt. 6, 125 (1994); P. Kasperkovitz and M. Peev, Ann. Phys. (N.Y.) 230, 21 (1994); U. Leonhardt, Phys. Rev. Lett. 74, 4101 (1995); Phys. Rev. A 53, 2998 (1996); T. Opatrný, D.-G. Welsch, and B. Bužek, ibid. 53, 3822 (1996); A. Luis and J. Peøina, J. Phys. A 31, 1423 (1998); C. Miquel, J. P. Paz, and M. Saraceno, ibid. 65, 062309 (2002); J. P. Paz, ibid. 65, 062311 (2002).
[7] K. Vogel and H. Risken, Phys. Rev. A 40, 2847 (1989); D. T. Smithey, M. Beck, M. G. Raymer, and A. Faridani, Phys. Rev. Lett. 70, 1244 (1993); S. Schiller, G. Breitenbach, S. F. Pereira, T. Müller, and J. Mlynek, ibid. 77, 2933 (1996); G. Breitenbach, S. Schiller, and J. Mlynek, Nature (London) 387, 471 (1997).
[8] G. GarcÃa Calderón and M. Moshinsky, J. Phys. A 13, L185 (1980); R. Dirl, P. Kasperkovitz, and M. Moshinsky, ibid. 21, 1835 (1988); A. K. Ekert and P. L. Knight, Phys. Rev. A 43, 3934 (1991).
[9] A. Walther, J. Opt. Soc. Am. 58, 1256 (1968); M. J. Bastiaans, Opt. Commun. 25, 26 (1978); 30, 321 (1979); J. Opt. Soc. Am. A 3, 1227 (1986); R. Simon, E. C. G. Sudarshan, and N. Mukunda, Phys. Rev. A 29, 3273 (1984); D. Dragoman, in Progress in Optics, edited by E. Wolf (North-Holland, Amsterdam, 1997), Vol. 37, p. 1; G. S. Agarwal, J. T. Foley, and E. Wolf, Opt. Commun. 62, 67 (1987); R. Simon, N. Mukunda, and E. C. G. Sudarshan, ibid. 65, 322 (1988); special issue on Wigner function in optics [J. Opt. Soc. Am. A 17(12), 2274 (2000)].
[10] J. F. Poyatos, J. I. Cirac, and P. Zoller, Phys. Rev. Lett. 78, 390 (1997); I. L. Chuang and M. A. Nielsen, J. Mod. Opt. 44, 2455 (1997); G. M. D’Ariano and L. Maccone, Phys. Rev. Lett. 80, 5465 (1998); V. Bužek, Phys. Rev. A 58, 1723 (1998); R. Gutzeit, S. Wallentowitz, and W. Vogel, ibid. 61, 062105 (2000); A. M. Childs, I. L. Chuang, and D. W. Leung, ibid. 64, 012314 (2001); J. Fiurášek and Z. Hradil, ibid. 63, 020101(R) (2001); J. Fiurášek, ibid. 64, 024102 (2001); G. M. D’Ariano and P. Lo Presti, Phys. Rev. Lett. 86, 4195 (2001); e-print quant-ph/0211133; F. De Martini, A. Mazzei, M. Ricci, and G. D’Ariano, e-print quant-ph/0210210; J. B. Altepeter, D. Branning, E. Jeffrey, T. C. Wei, P. G. Kwiat, R. T. Thew, J. L. O’Brien, M. A. Nielsen, and A. G. White, Phys. Rev. Lett. 90, 193601 (2003).
[11] A. Luis and L. L. Sánchez-Soto, Phys. Lett. A 261, 12 (1999); Phys. Rev. Lett. 83, 3573 (1999); A. Luis, Phys. Rev. A 62, 054302 (2000).
[12] J. D. Gaskill, Linear Systems, Fourier Transforms and Optics (Wiley, New York, 1978); J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1996).
[13] J. Peøina, Quantum Statistics of Linear and Nonlinear Optical Phenomena, 2nd ed. (Kluwer Academic, Dordrecht, 1991).
[14] L. Knöll, S. Scheel, E. Schmidt, D.-G. Welsch, and A. V. Chizhov, Phys. Rev. A 59, 4716 (1999).
[15] M. Khanbekyan, L. Knöll, A. A. Semenov, W. Vogel, and D.-G. Welsch, Phys. Rev. A 69, 043807 (2004).
[16] U. Fano, Rev. Mod. Phys. 29, 74 (1957); A. Royer, Phys. Rev. A 43, 44 (1991).
[17] M. Wilkens and P. Meystre, Phys. Rev. A 43, 3832 (1991); S. M. Dutra P. L. Knight, and H. Moya-Cessa, ibid. 48, 3168 (1993); S. M. Dutra and P. L. Knight, ibid. 49, 1506 (1994); M. S. Kim, G. Antesberger, C. T. Bodendorf, and H. Walther, ibid. 58, R65 (1998); P. J. Bardroff, M. T. Fontenelle, and S. Stenholm, ibid. 59, R950 (1999); M. S. Kim and G. S. Agarwal, ibid. 59, 3044 (1999).
[18] C. M. Caves, Phys. Rev. D 26, 1817 (1982).
[19] S. Wallentowitz and W. Vogel, Phys. Rev. A 55, 4438 (1997).