Effect of fluctuation measures on the uncertainty relations between two observables: Different measures lead to opposite conclusions

Physical Review A - Atomic, Molecular, and Optical Physics

Volumn 84, Issue 3, 2011, Pages

  Luis, Alfredo ^a  

^a UNIVERSIDAD COMPLUTENSE DE MADRID   (Spain)

Author keywords

[No Author keywords available]

Indexed keywords

JOINT UNCERTAINTY; UNCERTAINTY RELATION;

EID: 80052742102     PISSN: 10502947     EISSN: 10941622     Source Type: Journal    
DOI: 10.1103/PhysRevA.84.034101     Document Type: Article

References (44)

1. J. Hilgevoord, Am. J. Phys. AJPIAS 0002-9505 10.1119/1.1503380 70, 983 (2002);
2. G. N. Lawrence, Laser Focus World 30, 109 (1994);
3. J. Řehàček and Z. Hradil, J. Mod. Opt. JMOPEW 0950-0340 10.1080/09500340408233612 51, 979 (2004).
4. A. Luis, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.64.012103 64, 012103 (2001);
5. A. Luis, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.67.032108 67, 032108 (2003).
6. J. M. Lévy-Leblond, Ann. Phys. (NY) APNYA6 0003-4916 10.1016/0003-4916(76)90283-9 101, 319 (1976);
7. E. Breitenberger, Found. Phys. FNDPA4 0015-9018 10.1007/BF00737323 15, 353 (1985);
8. J. B. M. Uffink, Phys. Lett. A PYLAAG 0375-9601 10.1016/0375-9601(85) 90516-X 108, 59 (1985);
9. J. M. Lévy-Leblond, Phys. Lett. A PYLAAG 0375-9601 10.1016/0375-9601(85)90367-6 111, 353 (1985);
10. S. M. Barnett and D. T. Pegg, J. Mod. Opt. JMOPEW 0950-0340 10.1080/09500348914550021 36, 7 (1989);
11. Z. Hradil, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.46.R2217 46, R2217 (1992);
12. Z. Hradil, Quantum Opt. QUOPET 0954-8998 10.1088/0954-8998/4/2/004 4, 93 (1992);
13. T. Opatrný, J. Phys. A JPHAC5 0305-4470 10.1088/0305-4470/27/21/ 034 27, 7201 (1994);
14. V. Peřinová, A. Lukš, and J. Peřina, Phase in Optics (World Scientific, Singapore, 1998).
15. I. I. Hirschman, Am. J. Math. AJMAAN 0002-9327 10.2307/2372390 79, 152 (1957);
16. I. Bialynicki-Birula and J. Mycielski, Commun. Math. Phys. CMPHAY 0010-3616 10.1007/BF01608825 44, 129 (1975);
17. D. Deutsch, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.50.631 50, 631 (1983);
18. M. H. Partovi, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.50. 1883 50, 1883 (1983);
19. K. Kraus, Phys. Rev. D PRVDAQ 1550-7998 10.1103/PhysRevD.35.3070 35, 3070 (1987);
20. H. Maassen and J. B. M. Uffink, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.60.1103 60, 1103 (1988);
21. J. Sanchez, Phys. Lett. A PYLAAG 0375-9601 10.1016/0375-9601(93)90269-6 173, 233 (1993);
22. Č. Brukner and A. Zeilinger, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.83.3354 83, 3354 (1999);
23. Č. Brukner and A. Zeilinger, Phys. Rev. A 1050-2947 10.1103/PhysRevA.63.022113 63, 022113 (2001);
24. V. Majerník and E. Majerníková, Rep. Math. Phys. RMHPBE 0034-4877 10.1016/S0034-4877(01)80051-3 47, 381 (2001); (Pubitemid 33668100)
25. M. J. W. Hall, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.64.052103 64, 052103 (2001);
26. S. Massar and P. Spindel, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.100.190401 100, 190401 (2008); (Pubitemid 351671507)
27. S. Wehner and A. Winter, New J. Phys. NJOPFM 1367-2630 10.1088/1367-2630/12/2/025009 12, 025009 (2010);
28. I. Bialynicki-Birula and L. Rudnicki, e-print arXiv: 1001.4668v1;
29. I. Urizar-Lanz and G. Tóth, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.81.052108 81, 052108 (2010);
30. P. Sánchez-Moreno, A. R. Plastino, and J. S. Dehesa, J. Phys. A PLRAAN 1751-8113 10.1088/1751-8113/44/6/065301 44, 065301 (2011);
31. A. E. Rastegin, J. Phys. A PLRAAN 1751-8113 10.1088/1751-8113/44/9/095303 44, 095303 (2011).
32. C. Tsallis, J. Stat. Phys. JSTPBS 0022-4715 10.1007/BF01016429 52, 479 (1988);
33. E. M. F. Curado and C. Tsallis, J. Phys. A JPHAC5 0305-4470 10.1088/0305-4470/24/2/004 24, L69 (1991);
34. A. K. Rajagopal, Phys. Lett. A PYLAAG 0375-9601 10.1016/0375-9601(95) 00500-3 205, 32 (1995).
35. M. Portesi and A. Plastino, Physica A PHYADX 0378-4371 10.1016/0378-4371(95)00475-0 225, 412 (1996).
36. 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;
37. U. Larsen, J. Phys. A JPHAC5 0305-4470 10.1088/0305-4470/23/7/013 23, 1041 (1990);
38. I. Bialynicki-Birula, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.74. 052101 74, 052101 (2006). (Pubitemid 44674157)
39. A. Luis, Opt. Lett. OPLEDP 0146-9592 10.1364/OL.31.003644 31, 3644 (2006); (Pubitemid 46079730)
40. A. Luis, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.75.052115 75, 052115 (2007). (Pubitemid 47014521)
41. S. Zozor, M. Portesi, and C. Vignat, Physica A PHYADX 0378-4371 10.1016/j.physa.2008.04.010 387, 4800 (2008).
42. A. Luis, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.80.034101 80, 034101 (2009).
43. Z. Hradil, R. Myška, T. Opatrný, and J. Bajer, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.53.3738 53, 3738 (1996);
44. G. A. Durkin and J. P. Dowling, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.99.070801 99, 070801 (2007). (Pubitemid 47267861)