Metric character of the quantum Jensen-Shannon divergence

被引：121

作者：

Lamberti, P. W. ^{[1
,2
]}

Majtey, A. R. ^{[3
,4
]}

Borras, A. ^{[3
,4
]}

Casas, M. ^{[3
,4
]}

Plastino, A. ^{[2
,5
]}

机构：

[1] Univ Nacl Cordoba, Fac Matemat Astron & Fis, RA-5000 Cordoba, Argentina

[2] Consejo Nacl Invest Cient & Tecn, RA-1900 La Plata, Argentina

[3] Univ Illes Balears, Dept Fis, Palma de Mallorca 07122, Spain

[4] Univ Illes Balears, IFISC, Palma de Mallorca 07122, Spain

[5] Natl Univ La Plata, Inst Fis La Plata, RA-1900 La Plata, Argentina

来源：

PHYSICAL REVIEW A | 2008年 / 77卷 / 05期

关键词：

D O I：

10.1103/PhysRevA.77.052311

中图分类号：

O43 [光学];

学科分类号：

070207 ; 0803 ;

摘要：

In a recent paper, the generalization of the Jensen-Shannon divergence in the context of quantum theory has been studied [Majtey et al., Phys. Rev. A 72, 052310 (2005)]. This distance between quantum states has shown to verify several of the properties required for a good distinguishability measure. Here we investigate the metric character of this distance. More precisely we show, formally for pure states and by means of a numerical procedure for mixed states, that its square root verifies the triangle inequality.

引用

页数：6

共 28 条

[1] Metrics, entanglement, and mixedness in the space of two-qubits [J].

Batle, J ;

Casas, M ;

Plastino, A ;

Plastino, AR .

PHYSICS LETTERS A, 2006, 353 (2-3) :161-165

[2]

Bengtsson I., 2017, Geometry of quantum states: an introduction to quantum entanglement, V2nd, DOI DOI 10.1017/9781139207010

[3] STATISTICAL DISTANCE AND THE GEOMETRY OF QUANTUM STATES [J].

BRAUNSTEIN, SL ;

CAVES, CM .

PHYSICAL REVIEW LETTERS, 1994, 72 (22) :3439-3443

[4] Measuring thermodynamic length [J].

Crooks, Gavin E. .

PHYSICAL REVIEW LETTERS, 2007, 99 (10)

[5] ON THE RELATIVE ENTROPY [J].

DONALD, MJ .

COMMUNICATIONS IN MATHEMATICAL PHYSICS, 1986, 105 (01) :13-34

[6] A new metric for probability distributions [J].

Endres, DM ;

Schindelin, JE .

IEEE TRANSACTIONS ON INFORMATION THEORY, 2003, 49 (07) :1858-1860

[7]

Fuglede B, 2004, 2004 IEEE INTERNATIONAL SYMPOSIUM ON INFORMATION THEORY, PROCEEDINGS, P31

[8] Information and computation:: Classical and quantum aspects [J].

Galindo, A ;

Martín-Delgado, MA .

REVIEWS OF MODERN PHYSICS, 2002, 74 (02) :347-423

[9]

Grosse I, 2002, PHYS REV E, V65, DOI 10.1103/PhysRevE.65.041905

[10] FIDELITY FOR MIXED QUANTUM STATES [J].

JOZSA, R .

JOURNAL OF MODERN OPTICS, 1994, 41 (12) :2315-2323

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