Classical and quantum Fisher information in the geometrical formulation of quantum mechanics

被引：77

作者：

Facchi, Paolo ^{[2
,3
,4
]}

Kulkarni, Ravi ^{[5
]}

Man'ko, V. I. ^{[1
]}

Marmo, Giuseppe ^{[4
,6
,7
]}

Sudarshan, E. C. G. ^{[8
]}

Ventriglia, Franco ^{[4
,6
,7
]}

机构：

[1] PN Lebedev Phys Inst, Moscow 119991, Russia

[2] Univ Bari, Dipartimento Matemat, I-70125 Bari, Italy

[3] Ist Nazl Fis Nucl, Sez Bari, I-70126 Bari, Italy

[4] Univ Naples Federico II, MECENAS, Naples, Italy

[5] Vivekananda Yoga Res Fdn, Bangalore 560080, Karnataka, India

[6] Univ Naples Federico II, Dipartimento Sci Fis, I-80126 Naples, Italy

[7] Ist Nazl Fis Nucl, Sez Napoli, I-80126 Naples, Italy

[8] Univ Texas Austin, Dept Phys, Austin, TX 78712 USA

来源：

PHYSICS LETTERS A | 2010年 / 374卷 / 48期

关键词：

GEOMETRIZATION;

D O I：

10.1016/j.physleta.2010.10.005

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

The tomographic picture of quantum mechanics has brought the description of quantum states closer to that of classical probability and statistics On the other hand the geometrical formulation of quantum mechanics introduces a metric tensor and a symplectic tensor (Hermitian tensor) on the space of pure states By putting these two aspects together we show that the Fisher information metric both classical and quantum can be described by means of the Hermitian tensor on the manifold of pure states (C) 2010 Elsevier B V All rights reserved

引用

页码：4801 / 4803

页数：3

共 20 条

[1] CLASSICAL TENSORS AND QUANTUM ENTANGLEMENT I: PURE STATES
Aniello, P.
Clemente-Gallardo, J.
Marmo, G.
Volkert, G. F.
[J]. INTERNATIONAL JOURNAL OF GEOMETRIC METHODS IN MODERN PHYSICS, 2010, 7 (03) : 485 - 503
[2] CLASSICAL TENSORS FROM QUANTUM STATES
Aniello, P.
Marmo, G.
Volkert, G. F.
[J]. INTERNATIONAL JOURNAL OF GEOMETRIC METHODS IN MODERN PHYSICS, 2009, 6 (03) : 369 - 383
[3] STATISTICAL DISTANCE AND THE GEOMETRY OF QUANTUM STATES
BRAUNSTEIN, SL
CAVES, CM
[J]. PHYSICAL REVIEW LETTERS, 1994, 72 (22) : 3439 - 3443
[4] Geometrization of statistical mechanics
Brody, DC
Hughston, LP
[J]. PROCEEDINGS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES, 1999, 455 (1985): : 1683 - 1715
[5] Geometrization of quantum mechanics
Carinena, J. F.
Clemente-Gallardo, J.
Marmo, G.
[J]. THEORETICAL AND MATHEMATICAL PHYSICS, 2007, 152 (01) : 894 - 903
[6] Remarks on the GNS Representation and the Geometry of Quantum States
Chruscinski, Dariusz
Marmo, Giuseppe
[J]. OPEN SYSTEMS & INFORMATION DYNAMICS, 2009, 16 (2-3) : 157 - 177
[7] Wigner-Yanase information on quantum state space: The geometric approach
Gibilisco, P
Isola, T
[J]. JOURNAL OF MATHEMATICAL PHYSICS, 2003, 44 (09) : 3752 - 3762
[8] Geometry of quantum systems: density states and entanglement
Grabowski, J
Kus, M
Marmo, G
[J]. JOURNAL OF PHYSICS A-MATHEMATICAL AND GENERAL, 2005, 38 (47): : 10217 - 10244
[9] MINIMUM MEAN-SQUARED ERROR OF ESTIMATES IN QUANTUM STATISTICS
HELSTROM, CW
[J]. PHYSICS LETTERS A, 1967, A 25 (02) : 101 - &
[10] Holevo A. S., 1982, Probabilistic and statistical aspect of quantum theory

← 1 2 →