RT Journal Article T1 Effect of fluctuation measures on the uncertainty relations between two observables: different measures lead to opposite conclusions A1 Luis Aina, Alfredo AB We show within a very simple framework that different measures of fluctuations lead to uncertainty relations resulting in contradictory conclusions. More specifically we focus on Tsallis and Renyi entropic uncertainty relations and we get that the minimum joint uncertainty states for some fluctuation measures are the maximum joint uncertainty states of other fluctuation measures, and vice versa. PB American Physical Society SN 1050-2947 YR 2011 FD 2011-09-14 LK https://hdl.handle.net/20.500.14352/44598 UL https://hdl.handle.net/20.500.14352/44598 LA eng NO [1] J. Hilgevoord, Am. J. Phys. 70, 983 (2002); G. N. Lawrence, Laser Focus World 30, 109 (1994); J. Rӗha`cӗk and Z. Hradil, J. Mod. Opt. 51, 979 (2004).[2] A. Luis, Phys. Rev. A 64, 012103 (2001); 67, 032108 (2003).[3] J. M. Lévy-Leblond, Ann. Phys. (NY) 101, 319 (1976); E. Breitenberger, Found. Phys. 15, 353 (1985); J. B. M. Uffink, Phys. Lett. A 108, 59 (1985); J. M. Lévy-Leblond, ibid. 111, 353 (1985); S. M. Barnett and D. T. Pegg, J. Mod. Opt. 36, 7 (1989); Z. Hradil, Phys. Rev. A 46, R2217 (1992); Quantum Opt. 4, 93 (1992); T. Opatrn´y, J. Phys. A 27, 7201 (1994); V. Peřinová, A. Lukš, and J. Peřina, Phase in Optics (World Scientific, Singapore, 1998).[4] I. I. Hirschman, Am. J. Math. 79, 152 (1957); I. Bialynicki-Birula and J. Mycielski, Commun. Math. Phys. 44, 129 (1975); D. Deutsch, Phys. Rev. Lett. 50, 631 (1983); M. H. Partovi, ibid. 50, 1883 (1983); K. Kraus, Phys. Rev. D 35, 3070 (1987); H. Maassen and J. B. M. Uffink, Phys. Rev. Lett. 60, 1103 (1988); J. Sanchez, Phys. Lett. A 173, 233 (1993); Č . Brukner and A. Zeilinger, Phys. Rev. Lett. 83, 3354 (1999); Phys. Rev. A 63, 022113 (2001); V. Majerník and E. Majerníková, Rep. Math. Phys. 47, 381 (2001); M. J. W. Hall, Phys. Rev. A 64, 052103 (2001); S. Massar and P. Spindel, Phys. Rev. Lett. 100, 190401 (2008); S. Wehner and A. Winter, New J. Phys. 12, 025009 (2010); I. Bialynicki-Birula and L. Rudnicki, e-print arXiv:1001.4668v1; I. Urizar-Lanz and G. Tóth, Phys. Rev. A 81, 052108 (2010); P. Sánchez-Moreno, A. R. Plastino, and J. S. Dehesa, J. Phys. A 44, 065301 (2011); A. E. Rastegin, ibid. 44, 095303 (2011).[5] C. Tsallis, J. Stat. Phys. 52, 479 (1988); E. M. F. Curado and C. Tsallis, J. Phys. A 24, L69 (1991); A. K. Rajagopal, Phys. Lett. A 205, 32 (1995).[6] M. Portesi and A. Plastino, Physica A 225, 412 (1996).[7] A. Renyi, in Proceedings of the 4th Berkeley Symposium on Mathematics and Staticstical Probability, Vol. 1 (University of California Press, Berkeley, California, 1961), pp. 547–561; U. Larsen, J. Phys. A 23, 1041 (1990); I. Bialynicki-Birula, Phys. Rev. A 74, 052101 (2006).[8] A. Luis, Opt. Lett. 31, 3644 (2006); Phys. Rev. A 75, 052115 (2007).[9] S. Zozor,M. Portesi, and C.Vignat, PhysicaA387, 4800 (2008).[10] A. Luis, Phys. Rev. A 80, 034101 (2009).[11] Z. Hradil, R. Myška, T. Opatrný, and J. Bajer, Phys. Rev. A 53, 3738 (1996); G. A. Durkin and J. P. Dowling, Phys. Rev. Lett. 99, 070801 (2007). NO ©2011 American Physical Society. A.L. acknowledges support from Project No. FIS2008-01267 of the Spanish Direccion General de Investigacion del Ministerio de Ciencia e Innovacion, and from Project QUITEMAD S2009-ESP-1594 of the Consejeria de Educacion de la Comunidad de Madrid. NO Ministerio de Ciencia e Innovacion (MICINN), España NO Comunidad de Madrid DS Docta Complutense RD 30 abr 2024