Informationally complete measurements and group representation

被引：89

作者：

D'Ariano, GM

Perinotti, P

Sacchi, MF

机构：

[1] Univ Pavia, Unita INFM, I-27100 Pavia, Italy

[2] Univ Pavia, Dipartimento Fis A Volta, I-27100 Pavia, Italy

来源：

JOURNAL OF OPTICS B-QUANTUM AND SEMICLASSICAL OPTICS | 2004年 / 6卷 / 06期

关键词：

quantum measurements; operator spaces; frames; groups; covariant POVMs;

D O I：

10.1088/1464-4266/6/6/005

中图分类号：

O43 [光学];

学科分类号：

070207 ; 0803 ;

摘要：

Informationally complete measurements on a quantum system allow one to estimate the expectation value of any arbitrary operator by just averaging functions of the experimental outcomes. We show that such kinds of measurement can be achieved through positive-operator valued measures (POVMs) related to unitary irreducible representations of a group on the Hilbert space of the system. With the help of frame theory we provide a constructive way to evaluate the data-processing function for arbitrary operators.

引用

页码：S487 / S491

页数：5

共 25 条

[1] SUFFICIENT CONDITIONS FOR CONVERGENCE OF ANTINORMALLY ORDERED EXPANSIONS OF BOSON NUMBER OPERATOR-FUNCTIONS F(A+A) [J].

BALTIN, R .

JOURNAL OF PHYSICS A-MATHEMATICAL AND GENERAL, 1983, 16 (12) :2721-2742

[2] INFORMATIONALLY COMPLETE-SETS OF PHYSICAL QUANTITIES [J].

BUSCH, P .

INTERNATIONAL JOURNAL OF THEORETICAL PHYSICS, 1991, 30 (09) :1217-1227

[3]

BUSCH P, 1995, SPRINGER LECT NOTES, V31, P32114

[4] ORDERED EXPANSIONS IN BOSON AMPLITUDE OPERATORS [J].

CAHILL, KE ;

GLAUBER, RJ .

PHYSICAL REVIEW, 1969, 177 (5P1) :1857-+

[5] The art of frame theory [J].

Casazza, PG .

TAIWANESE JOURNAL OF MATHEMATICS, 2000, 4 (02) :129-201

[6] Unknown quantum states: The quantum de Finetti representation [J].

Caves, CM ;

Fuchs, CA ;

Schack, R .

JOURNAL OF MATHEMATICAL PHYSICS, 2002, 43 (09) :4537-4559

[7] Bell measurements and observables [J].

D'Ariano, GM ;

Lo Presti, P ;

Sacchi, MF .

PHYSICS LETTERS A, 2000, 272 (1-2) :32-38

[8]

D'Ariano GM, 2003, PROCEEDINGS OF THE 8TH INTERNATIONAL CONFERENCE ON SQUEEZED STATES AND UNCERTAINTY RELATIONS, P86

[9] Quantum tomography [J].

D'Ariano, GM ;

Paris, MGA ;

Sacchi, MF .

ADVANCES IN IMAGING AND ELECTRON PHYSICS, VOL 128, 2003, 128 :205-308

[10] Adaptive quantum homodyne tomography [J].

D'Ariano, GM ;

Paris, MGA .

PHYSICAL REVIEW A, 1999, 60 (01) :518-528

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