RT Journal Article
T1 Complementarity and duality relations for finite-dimensional systems
A1 Luis Aina, Alfredo
AB We generalize to systems with arbitrary finite dimension a measure of quantum fluctuations (the certainty) previously introduced for two-dimensional systems. Using this measure, we study the duality relations satisfied by complementary observables looking for states with minimum joint fluctuations (maximum certainty states). We extend the duality relations to encompass several complementary observables simultaneously.
PB American Physical Society
SN 1050-2947
YR 2003
FD 2003-03-19
LK https://hdl.handle.net/20.500.14352/51522
UL https://hdl.handle.net/20.500.14352/51522
LA eng
NO [1] C.W. Helstrom, Quantum Detection and Estimation Theory (Academic Press, New York, 1976); A. Peres, Found. Phys. 20, 1441 (1990); Quantum Theory: Concepts and Methods (Kluwer Academic, Dordrecht, 1993).[2] J.M. Lévy-Leblond, Ann. Phys. (N.Y.) 101, 319 (1976); E. Breitenberger, Found. Phys. 15, 353 (1985); J.B.M. Uffink, Phys. Lett. 108A, 59 (1985); J.M. Lévy-Leblond, ibid. 111, 353 (1985); Z. Hradil, Phys. Rev. A 46, R2217 (1992); Quantum Opt. 4, 93 (1992); T. Opatrný, J. Phys. A 27, 7201 (1994).[3] V. Peřinová, A. Lukš, and J. Peřina, Phase in Optics (World Scientific, Singapore, 1998).[4] S.M. Barnett and D.T. Pegg, J. Mod. Opt. 36, 7 (1989).[5] A. Luis, Phys. Rev. A 64, 012103 (2001), and references therein.[6] I. Bialynicki-Birula and J. Mycielski, Commun. Math. Phys. 44, 129 (1975).[7] D. Deutsch, Phys. Rev. Lett. 50, 631 (1983); M.H. Partovi, ibid. 50, 1883 (1983); K. Kraus, Phys. Rev. D 35, 3070 (1987).[8] J.H. Shapiro and S.R. Shepard, Phys. Rev. A 43, 3795 (1991); M.J.W. Hall, J. Mod. Opt. 40, 809 (1993).[9] E.J. Heller, Phys. Rev. A 35, 1360 (1987); H. Maassen and J.B.M. Uffink, Phys. Rev. Lett. 60, 1103 (1988); I. Bialynicki-Birula, M. Freyberger, and W. Schelich, Phys. Scr., T 48, 113 (1993); A. Anderson and J.J. Halliwell, Phys. Rev. D 48, 2753 (1993); A. Lukš and V. Peřinová, Quantum Opt. 6, 125 (1994); A. Orlowski, H. Paul, and B. Böhmer, Opt. Commun. 138, 311 (1997); B. Mirbach and H.J. Korsch, Ann. Phys. (N.Y.) 265, 80 (1998); M.J.W. Hall, Phys. Rev. A 59, 2602 (1999); G. Manfredi and M.R. Feix, Phys. Rev. E 62, 4665 (2000); A. Sugita and H. Aiba, e-print nlin.CD/0106012; S. Gnutzmann and K. Życzkowski, J. Phys. A 34, 10 123 (2001); S. Dürr, Phys. Rev. A 64, 042113 (2001); A. Luis, ibid. 66, 013806 (2002); J. Phys. A 35, 8805 (2002).[10] A. Luis, Phys. Rev. Lett. 88, 230401 (2002).[11] U. Larsen, J. Phys. A 23, 1041 (1990).[12] Č. Brukner and A. Zeilinger, Phys. Rev. Lett. 83, 3354 (1999); Phys. Rev. A 63, 022113 (2001); J. Řeháček and Z. Hradil, Phys. Rev. Lett. 88, 130401 (2002).[13] J. Peřina, Quantum Statistics of Linear and Nonlinear Optical Phenomena, 2nd ed. (Kluwer Academic, Dordrecht, 1991).[14] M.O. Scully, B.-G. Englert, and H. Walther, Nature (London) 351, 111 (1991).[15] J. Sánchez, Phys. Lett. A 173, 233 (1993).[16] J. Sánchez-Ruiz, Phys. Lett. A 201, 125 (1995).[17] A. Luis and L.L. Sánchez-Soto, in Progress in Optics, edited by E. Wolf (Elsevier, Amsterdam, 2000), Vol. 41, p. 421.[18] F.T. Arecchi, E. Courtens, R. Gilmore, and H. Thomas, Phys. Rev. A 6, 2211 (1972).[19] A.J. Leggett and F. Sols, Found. Phys. 21, 353 (1991); Y. Castin and J. Dalibard, Phys. Rev. A 55, 4330 (1997); A. Sinatra and Y. Castin, Eur. Phys. J. D 4, 247 (1998).[20] A. Wünsche, Acta Phys. Slov. 49, 771 (1999); J. Opt. B: Quantum Semiclassical Opt. 3, 206 (2001).[21] B. Baseia, A.F. de Lima, and G.C. Marques, Phys. Lett. A 204, 1 (1995); A.F. de Lima, B. Baseia, and G.C. Marques, J. Mod. Opt. 43, 729 (1996).[22] W.K. Wootters and B.D. Fields, Ann. Phys. (N.Y.) 191, 363 (1989).[23] H.P. Robertson, Phys. Rev. 46, 794 (1934); D.A. Trifonov, J. Phys. A 33, L299 (2000); 34, L75 (2001).[24] I.D. Ivanovic, J. Phys. A 25, L363 (1992).[25] A.R. González, J.A. Vaccaro, and S.M. Barnett, Phys. Lett. A 205, 247 (1995).
NO ©2003 The American Physical Society
DS Docta Complutense
RD 27 abr 2024