Uncertainty principle with quantum Fisher information

Journal of Mathematical Physics

Volumn 49, Issue 1, 2008, Pages

  Andai, Attila ^a  

^a RIKEN BRAIN SCIENCE INSTITUTE   (Japan)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 38849107497     PISSN: 00222488     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.2830429     Document Type: Article

References (22)

1. E. Beckenbach and R. Bellman, Inequalities (Springer, Berlin, 1961).
2. W. J. Firey, " Some applications of means of convex bodies.," Pac. J. Math. PJMAAI 0030-8730 14, 53-60 (1964).
3. P. Gibilisco, D. Imparato, and T. Isola, " Uncertainty principle and quantum Fisher information II.," J. Math. Phys. JMAPAQ 0022-2488 10.1063/1.2748210 48, 072109 (2007).
4. P. Gibilisco, D. Imparato, and T. Isola, " A volume inequality for quantum Fisher information and the uncertainty principle.," J. Stat. Phys. JSTPBS 0022-4715 10.1007/s10955-007-9454-2 130, 545-559 (2007).
5. P. Gibilisco, D. Imparato, and T. Isola, " A Robertson-type uncertainty principle and quantum Fisher information.," e-print arXiv:math-ph/0707.1231v1 (2007).
6. P. Gibilisco and T. Isola, " Uncertainty principle and quantum Fisher information.," Ann. Inst. Stat. Math. AISXAD 0020-3157 10.1007/s10463-006-0103-3 59, 147-159 (2006).
7. F. Hansen, " Metric adjusted skew information.," e-print arXiv:math-ph/0607049v5 (2007).
8. W. Heisenberg, " Über den anschaulichen inhalt der quantentheoretischen kinematik und mechanik.," Z. Phys. ZEPYAA 0044-3328 10.1007/BF01397280 43, 172-198 (1927).
9. F. Hiai, D. Petz, and G. Toth, " Curvature in the geometry of canonical correlation.," Stud. Sci. Math. Hung. SSMHAX 0081-6906 32, 235-249 (1996).
10. R. A. Horn and C. R. Johnson, Matrix Analysis (Cambridge University Press, Cambridge, 1985).
11. H. Kosaki, " Matrix trace inequality related to uncertainty principle.," Int. J. Math. ZZZZZZ 0129-167X 16, 629-645 (2005).
12. S. Luo, " Quantum Fisher information and uncertainty relations.," Lett. Math. Phys. LMPHDY 0377-9017 10.1023/A:1011080128419 53, 243-251 (2000).
13. S. Luo, " Wigner-Yanase skew information and uncertainty relations.," Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.91. 180403 91, 180403 (2003).
14. S. Luo and Q. Zhang, " On skew information.," IEEE Trans. Inf. Theory IETTAW 0018-9448 10.1109/TIT.2004.831853 50, 1778-1782 (2004).
15. S. Luo and Q. Zhang, " Correction to: On skew information.," IEEE Trans. Inf. Theory IETTAW 0018-9448 10.1109/TIT.2005.858974 51, 4432 (2005).
16. S. Luo and Z. Zhang, " An informational characterization of Schrödinger's uncertainty relations.," J. Stat. Phys. JSTPBS 0022-4715 10.1023/B:JOSS.0000013971.75667.c8 114, 1557-1576 (2004).
17. D. Petz, " Geometry of canonical correlation on the state space of a quantum system.," J. Math. Phys. JMAPAQ 0022-2488 10.1063/1.530611 35, 780-795 (1994).
18. D. Petz, " Monotone metrics on matrix spaces.," Numer. Linear Algebra Appl. ZZZZZZ 1070-5325 244, 81-96 (1996).
19. D. Petz, " Covariance and Fisher information in quantum mechanics.," J. Phys. A JPHAC5 0305-4470 35, 79-91 (2003).
20. D. Petz and Cs. Sudár, " On the curvature of a certain Riemannian space of matrices.," J. Math. Phys. JMAPAQ 0022-2488 10.1063/1.531535 37, 2662-2673 (1996).
21. E. Schrödinger, " About Heisenberg uncertainty relation.," Bulg. J. Phys. BJPHD5 0323-9217 26, 193-203 (2000); Translation of "Zum Heisenbergschen Unschärfeprinzip, Sitzungberichten der Preussischen Akademie der Wissenschaften," Sitzungsber. Preuss. Akad. Wiss., Phys. Math. Kl. SPWPAI 0371-2435 19, 296-303 (1930).
22. K. Yanagi, S. Furuichi, and K. Kuriyama, " A generalized skew information and uncertainty relation.," IEEE Trans. Inf. Theory IETTAW 0018-9448 10.1109/TIT.2005.858971 51, 4401-4404 (2005).