RT Journal Article
T1 Contradictions between different measures of quantum uncertainty
A1 Matia-Hernando, Paloma
A1 Luis Aina, Alfredo
AB We show that variance and Shannon entropy provide contradictory conclusions for the uncertainty associated with the number operator for some families of states of harmonic oscillator systems with fixed mean number, and for the uncertainty of a spin component for states with and without fixed mean. We analyze this behavior in terms of the properties of these uncertainty measures. We explore their impact on quantum metrology, examining the limits to resolution caused by number fluctuations in diverse scenarios of phase-shift detection.
PB American Physical Society
SN 1050-2947
YR 2012
FD 2012-11-09
LK https://hdl.handle.net/20.500.14352/44571
UL https://hdl.handle.net/20.500.14352/44571
LA eng
NO [1] S. L. Braunstein, Phys. Rev. Lett. 69, 3598 (1992); S. L. Braunstein and C. M. Caves, ibid. 72, 3439 (1994).[2] C.M. Caves, K. S. Thorne, R.W. P. Drever, V. D. Sandberg, and M. Zimmermann, Rev. Mod. Phys. 52, 341 (1980); C. M. Caves, Phys. Rev. D 23, 1693 (1981); M. J. Holland and K. Burnett, Phys. Rev. Lett. 71, 1355 (1993); M. Hillery and L. Mlodinow, Phys. Rev. A 48, 1548 (1993); J. J. Bollinger, W. M. Itano, D. J. Wineland, and D. J. Heinzen, ibid. 54, R4649 (1996); C. Brif and A. Mann, ibid. 54, 4505 (1996); Z. Y. Ou, ibid. 55, 2598 (1997); S. F. Huelga, C. Macchiavello, T. Pellizzari, A. K. Ekert, M. B. Plenio, and J. I. Cirac, Phys. Rev. Lett. 79, 3865 (1997); V. Giovannetti, S. Lloyd, and L. Maccone, Science 306, 1330 (2004); Phys. Rev. Lett. 108, 260405 (2012); M. J.W. Hall, D. W. Berry, M. Zwierz, and H. M. Wiseman, Phys. Rev. A 85, 041802(R) (2012); M. J. W. Hall and H. M. Wiseman, New J. Phys. 14, 033040 (2012); R. Nair, arXiv:1204.3761v1.[3] A. Rivas and A. Luis, New J. Phys. 14, 093052 (2012); A. Luis and A. Rodil, arXiv:1201.3072v1; A. Luis, arXiv:1203.4325v1.[4] A. Luis, Phys. Lett.A329, 8 (2004); SPIERev. 1, 018006 (2010); M. Napolitano, M. Koschorreck, B. Dubost, N. Behbood, R. J. Sewell, and M. W. Mitchell, Nature (London) 471, 486 (2011).[5] A. Rivas and A. Luis, Phys. Rev. Lett. 105, 010403 (2010).[6] J. Hilgevoord, Am. J. Phys. 70, 983 (2002); G. N. Lawrence, Laser Focus World 30, 109 (1994); J.  Řeháčk and Z. Hradil, J. Mod. Opt. 51, 979 (2004).[7] A. Luis, Phys. Rev. A 64, 012103 (2001); 67, 032108 (2003).[8] 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. Opatrný, J. Phys. A 27, 7201 (1994); V. Peřinová, A. Lukš, and J. Peřina, Phase inOptics (World Scientific, Singapore, 1998).[9] C. E. Shannon, Bell Syst. Tech. J. 27, 379 (1948); 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); M. J. W. Hall, ibid. 59, 2602 (1999); V. Majerník and E. Majerníková, Rep. Math. Phys. 47, 381 (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, Statistical Complexity, edited by K. D. Sen (Springer, Berlin, 2011), Chap. 1; A. E. Rastegin, J. Phys. A 44, 095303 (2011); Int. J. Theor. Phys. 51, 1300 (2012).[10] M. J. W. Hall, Phys. Rev. A 62, 012107 (2000); 64, 052103 (2001); P. Sánchez-Moreno, A. R. Plastino, and J. S. Dehesa, J. Phys. A 44, 065301 (2011).[11] A. Renyi, in Proceedings of the 4th Berkeley Symposium on Mathematics and Statistical Probability (University of California Press, Berkeley 1961), Vol. 1, pp. 547–561; C. Tsallis, J. Stat. Phys. 52, 479 (1988); U. Larsen, J. Phys. A 23, 1041 (1990); E. M. F. Curado and C. Tsallis, ibid. 24, L69 (1991); A. K. Rajagopal, Phys. Lett. A 205, 32 (1995); M. Portesi and A. Plastino, Physica A 225, 412 (1996); I. Bialynicki-Birula, Phys. Rev. A 74, 052101 (2006).[12] A. Luis, Opt. Lett. 31, 3644 (2006); Phys. Rev. A 75, 052115 (2007); S. Zozor, M. Portesi, and C. Vignat, Physica A 387, 4800 (2008).[13] A. Luis, Phys. Rev. A 84, 034101 (2011).[14] T. M. Cover and J. A. Thomas, Elements of Information Theory (Wiley Interscience, New York, 1991).[15] P. Réfrágier and F. Goudail, J. Opt. Soc. Am. A 23, 671 (2006); J. Solomon Ivan, M. Sanjay Kumar, and R. Simon, Quantum Inf. Proc. 11, 853 (2012); arXiv:0812.2800v1.[16] K. E. Cahill and R. J. Glauber, Phys. Rev. 177, 1857 (1969); 177, 1882 (1969); E. C. G. Sudarshan, Phys. Rev.A 23, 2802 (1981); L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge University Press,Cambridge, England, 1995); H.-W. Lee, Phys. Rep. 259, 147 (1995).[17] C. T. Lee, Phys. Rev. A 44, R2775 (1991); 52, 3374 (1995); A. F. de Lima and B. Baseia, ibid. 54, 4589 (1996); J. Janszky, M. G. Kim, and M. S. Kim, ibid. 53, 502 (1996).[18] J. A. Vaccaro, Opt. Commun. 113, 421 (1995); Phys. Rev. A 52, 3474 (1995); J. A.Vaccaro and D. T. Pegg, ibid. 41, 5156 (1990); L. M. Johansen, Phys. Lett. A 329, 184 (2004); J. Opt. B 6, L21 (2004); L. M. Johansen and A. Luis, Phys. Rev. A 70, 052115 (2004); A. Luis, ibid. 73, 063806 (2006).[19] R. L. Hudson, Rep. Math. Phys. 6, 249 (1974); M. Hillery, Phys. Lett. A 111, 409 (1985); N. Lütkenhaus and S.M. Barnett, Phys. Rev. A 51, 3340 (1995).[20] C. C. Gerry and P. L. Knight, Am. J. Phys. 65, 964 (1997).[21] F. T. Arecchi, E. Courtens, R. Gilmore, and H. Thomas, Phys. Rev. A 6, 2211 (1972).[22] O. Giraud, P. Braun, and D. Braun, Phys. Rev. A 78, 042112 (2008).[23] D. Martín and A. Luis, Phys. Rev. A 82, 033829 (2010).[24] A. P. Majtey, A. R. Plastino, and A. Plastino, Physica A 391, 2491 (2012).[25] H. Cramér, Mathematical Methods of Statistics (Asia Publishing House, Bombay, 1962).[26] J. Ziv and M. Zakai, IEEE Trans. Inf. Theory 15, 386 (1969); M. Tsang, Phys. Rev. Lett. 108, 230401 (2012); V. Giovannetti and L. Maccone, ibid. 108, 210404 (2012); Y. Gao and H. Lee, J. Phys. A 45, 415306 (2012).
NO ©2012 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 No. QUITEMAD S2009-ESP-1594 of the Consejeria de Educacion de la Comunidad de Madrid.
NO Ministerio de Ciencia e Innovacion (MICINN), España
NO Consejeria de Educacion de la Comunidad de Madrid
DS Docta Complutense
RD 7 may 2024