Commutative POVMs and Fuzzy Observables

被引：49

作者：

Ali, S. Twareque ^{[1
]}

Carmeli, Claudio ^{[2
,5
]}

Heinosaari, Teiko ^{[3
,4
]}

Toigo, Alessandro ^{[5
,6
]}

机构：

[1] Concordia Univ, Dept Math & Stat, Montreal, PQ H3G 1M8, Canada

[2] Univ Genoa, Dipartimento Fis, Genoa, Italy

[3] Univ Copenhagen, Niels Bohr Inst, DK-2100 Copenhagen, Denmark

[4] Univ Turku, Dept Phys, SF-20500 Turku, Finland

[5] Ist Nazl Fis Nucl, Sez Genova, I-16146 Genoa, Italy

[6] Univ Genoa, Dipartimento Informat, Genoa, Italy

来源：

FOUNDATIONS OF PHYSICS | 2009年 / 39卷 / 06期

关键词：

Commutative POVM; Fuzzy observable; Joint measurement; QUANTUM-MECHANICS;

D O I：

10.1007/s10701-009-9292-y

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

In this paper we review some properties of fuzzy observables, mainly as realized by commutative positive operator valued measures. In this context we discuss two representation theorems for commutative positive operator valued measures in terms of projection valued measures and describe, in some detail, the general notion of fuzzification. We also make some related observations on joint measurements.

引用

页码：593 / 612

页数：20

共 28 条

[1]

Ali S. T., 1982, Differential Geometric Methods in Mathematical Physics, P207, DOI [10.1007/BFb0092439, DOI 10.1007/BFB0092439]

[2] COMMUTATIVE SYSTEMS OF COVARIANCE AND A GENERALIZATION OF MACKEY IMPRIMITIVITY THEOREM [J].

ALI, ST .

CANADIAN MATHEMATICAL BULLETIN-BULLETIN CANADIEN DE MATHEMATIQUES, 1984, 27 (04) :390-397

[3] FUZZY OBSERVABLES IN QUANTUM-MECHANICS [J].

ALI, ST ;

EMCH, GG .

JOURNAL OF MATHEMATICAL PHYSICS, 1974, 15 (02) :176-182

[4]

[Anonymous], 1999, REAL ANAL MODERN TEC

[5]

[Anonymous], 1966, Van Nostrand Mathematical Studies No. 5

[6]

Busch P., 1997, Operational Quantum Physics

[7] Heisenberg's uncertainty principle [J].

Busch, Paul ;

Heinonen, Teiko ;

Lahti, Pekka .

PHYSICS REPORTS-REVIEW SECTION OF PHYSICS LETTERS, 2007, 452 (06) :155-176

[8]

Conway J. B., 1990, Graduate Texts in Mathematics, V96

[9]

Davies E. B., 1976, Quantum Theory of Open Systems

[10]

Davies E. B., 1970, J FUNCT ANAL, V6, P318, DOI DOI 10.1016/0022-1236(70)90064-9

← 1 2 3 →