Special Issue: Advances in Foundations of Quantum Mechanics and Quantum Information with atoms and photons, QUANTUM 2012No Access

STATE-EXTENDED UNCERTAINTY RELATIONS AND TOMOGRAPHIC INEQUALITIES AS QUANTUM SYSTEM STATE CHARACTERISTICS

V. N. CHERNEGA

P. N. Lebedev Physical Institute, Russian Academy of Sciences, Leninskii Prospect, 53, Moscow 119991, Russia

Search for more papers by this author

and

V. I. MAN'KO

P. N. Lebedev Physical Institute, Russian Academy of Sciences, Leninskii Prospect, 53, Moscow 119991, Russia

Search for more papers by this author

https://doi.org/10.1142/S0219749912410171Cited by:8 (Source: Crossref)

Abstract

Some inequalities for probability vector are discussed. The probability representation of quantum mechanics where the states are mapped onto probability vectors (either finite or infinite dimensional) called the state tomograms is used. Examples of inequalities for qudit tomograms and a state-extended uncertainty relation are considered. Tomographic cumulant related to photon state tomographic probability distributions is introduced and it is used as parameter of the state non-Gaussianity.

Keywords:

References

V. N. Chernega and V. I. Man'ko , J. Russ. Laser Res. 29 , 347 ( 2008 ) . Crossref, Web of Science, Google Scholar
V. N. Chernega and V. I. Man'ko , J. Russ. Laser Res. 30 , 359 ( 2009 ) . Crossref, Web of Science, Google Scholar
V. N. Chernega , Phys. Scr. T 147 , 014006 ( 2012 ) . Crossref, Google Scholar
S. Mancini , V. I. Man'ko and P. Tombesi , Phys. Lett. A 213 , 1 ( 1996 ) . Crossref, Web of Science, Google Scholar
A. Ibort et al. , Phys. Scr. 79 , 065013 ( 2009 ) . Crossref, Web of Science, Google Scholar
D. A. Trifonov , J. Phys. A: Math. Gen. 33 , L299 ( 2000 ) . Crossref, Google Scholar
D. A. Trifonov , Eur. Phys. J. B — Cond. Matter Complex Syst. 29 , 349 ( 2002 ) . Crossref, Web of Science, Google Scholar
M. Bellini et al. , Phys. Rev. A 85 , 052129 ( 2012 ) . Crossref, Web of Science, Google Scholar
V. I. Man'ko et al. , Phys. Scr. 83 , 04500 ( 2011 ) . Crossref, Web of Science, Google Scholar
D. T. Smithey et al. , Phys. Rev. Lett. 70 , 1244 ( 1993 ) . Crossref, Web of Science, Google Scholar
V. Parigi et al. , Science 317 , 1980 ( 2007 ) . Crossref, Web of Science, Google Scholar
V. N. Chernega and V. I. Man'ko , J. Russ. Laser Res. 28 , 103 ( 2007 ) . Crossref, Web of Science, Google Scholar
C. E. Shannon , Bell Syst. Tech. J. 27 , 379 ( 1948 ) . Crossref, Web of Science, Google Scholar
V. I. Man'ko et al. , Phys. Lett. A 327 , 353 ( 2004 ) . Crossref, Web of Science, Google Scholar
J. S. Bell , Physics 1 , 195 ( 1964 ) . Crossref, Google Scholar