RT Journal Article T1 Complementarity for generalized observables A1 Luis Aina, Alfredo AB We examine basic properties of complementarity by using the most general description of quantum observables as positive-operator measures. We show that, in general, two observables can be complementary or not depending on the measure of fluctuations adopted and that complementarity is not a symmetric relation. This occurs because the states that determine the measured statistics do not necessarily coincide with the minimum uncertainty states for the same observable. We also show that there are observables without a complementary observable and that complementarity is not preserved by the Neumark extensions. PB American Physical Society SN 0031-9007 YR 2002 FD 2002-06-10 LK https://hdl.handle.net/20.500.14352/59675 UL https://hdl.handle.net/20.500.14352/59675 LA eng NO [1] M. O. Scully, B.-G. Englert, and H. Walther, Nature (London) 351, 111 (1991).[2] X.Y. Zou, L. J. Wang, and L. Mandel, Phys. Rev. Lett. 67, 318 (1991); S. M. Tan and D. F. Walls, Phys. Rev. A 47, 4663 (1993); P. Storey, S. Tan, M. Collett, and D. Walls, Nature (London) 367, 626 (1994); B.-G. Englert, M. O. Scully, and H. Walther, ibid. 375, 367 (1995); E. P. Storey, S. M. Tan, M. J. Collett, and D. F. Walls, ibid. 375, 368 (1995); H. Wiseman and F. Harrison, ibid. 377, 584 (1995); B.-G. Englert, Phys. Rev. Lett. 77, 2154 (1996); L. S. Schulman, Phys. Lett. A 211, 75 (1996); H. M. Wiseman, F. E. Harrison, M. J. Collett, S. M. Tan, D. F. Walls, and R. B. Killip, Phys. Rev. A 56, 55 (1997); P. Knight, Nature (London) 395, 12 (1998); E. Buks, R. Schuster, M. Heiblum, D. Mahalu, and V. Umansky, ibid. 391, 871 (1998); S. Dürr, T. Nonn, and G. Rempe, ibid. 395, 33 (1998); Phys. Rev. Lett. 81, 5705 (1998); G. Björk, J. Söderholm, A. Trifonov, T. Tsegaye, and A. Karlsson, Phys. Rev. A 60, 1874 (1999); O. Steuernagel, quant-ph/9908011; A. Luis and L. L. Sánchez-Soto, Phys. Rev. Lett. 81, 4031 (1998); J. Opt. B 1, 668 (1999); S. Dürr and G. Rempe, Am. J. Phys. 68, 1021 (2000); P. Busch, P. Lahti, J.-P. Pellonpää, and K. Ylinen, J. Phys. A 34, 5923 (2001); P. Bertet, S. Osnaghi, A. Rauschenbeutel, G. Nogues, A. Auffeves, M. Brune, J. M. Raimond, and S. Haroche, Nature (London) 411, 166 (2001); M. Mei and M. Weitz, Phys. Rev. Lett. 86, 559 (2001); A. Luis, Phys. Rev. A 64, 012103 (2001); J. Phys. A 34, 8597 (2001); S. Dürr, Phys. Rev. A 64, 042113 (2001).[3] C.W. Helstrom, Quantum Detection and Estimation Theory (Academic, New York, 1976); A. Peres, Found. Phys. 20, 1441 (1990); Quantum Theory: Concepts and Methods (Kluwer Academic, Dordrecht, 1993).[4] T. S. Santhanam, Phys. Lett. 56A, 345 (1976); S. M. Barnett and D. T. Pegg, J. Mod. Opt. 36, 7 (1989); D. Ellinas, J. Math. Phys. (N.Y.) 32, 135 (1991).[5] A. Luis and L. L. Sánchez-Soto, Progress in Optics, edited by E. Wolf (Elsevier, Amsterdam, 2000), Vol. 41, p. 421.[6] M. Grabowski, Int. J. Theor. Phys. 28, 1215 (1989); Rep. Math. Phys. 29, 377 (1991).[7] I. Bialynicki-Birula, M. Freyberger, and W. Schleich, Phys. Scr. T48, 113 (1993); M. J.W. Hall, J. Mod. Opt. 40, 809 (1993).[8] J. H. Shapiro and S. R. Shepard, Phys. Rev. A 43, 3795 (1991).[9] Z. Hradil, Phys. Rev. A 46, R2217 (1992).[10] V. Peřinová, A. Lukš, and J. Peřina, Phase in Optics (World Scientific, Singapore, 1998).[11] J. M. Lévy-Leblond, Ann. Phys. (N.Y.) 101, 319 (1976); T. Opatrný, J. Phys. A 27, 7201 (1994).[12] A. Luis and J. Peřina, Phys. Rev. A 54, 4564 (1996).[13] F. T. Arecchi, E. Courtens, R. Gilmore, and H. Thomas, Phys. Rev. A 6, 2211 (1972).[14] M. Ban, Phys. Lett. A 152, 223 (1991); Opt. Commun. 94, 231 (1992); Phys. Lett. A 176, 47 (1993).[15] J. L. Park, Found. Phys. 1, 23 (1970); K. Kraus, Ann. Phys. (N.Y.) 64, 311 (1971); C. M. Caves and G. J. Milburn, Phys. Rev. A 36, 5543 (1987); B. d’Espagnat, ibid. 38, 5450 (1988); M. Ozawa, Phys. Lett. A 282, 336 (2001).[16] K. Banaszek, Phys. Rev. Lett. 86, 1366 (2001). NO © 2002 The American Physical Society DS Docta Complutense RD 7 may 2024