Renyi formulation of the entropic uncertainty principle for POVMs

被引：32

作者：

Rastegin, Alexey E. ^{[1
]}

机构：

[1] Irkutsk State Univ, Dept Theoret Phys, Irkutsk 664003, Russia

来源：

JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL | 2010年 / 43卷 / 15期

关键词：

QUANTUM MEASUREMENTS; NONCOMMUTING OBSERVABLES; INFORMATION; STATES; DIFFERENTIATE; INEQUALITY; SYSTEMS; SUM;

D O I：

10.1088/1751-8113/43/15/155302

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

Uncertainty relations for a pair of arbitrary measurements are posed in the form of inequalities using the Renyi entropies. The formulation deals with POVM measurements on finite-dimensional Hilbert space. Both the entropic uncertainty relations with state-dependent and state-independent bounds are presented. The results are illustrated on the example of measurements for state discrimination.

引用

页数：9

共 42 条

[1]

[Anonymous], 1982, N HOLLAND SERIES STA

[2] INEQUALITIES IN FOURIER-ANALYSIS [J].

BECKNER, W .

ANNALS OF MATHEMATICS, 1975, 102 (01) :159-182

[3] Formulation of the uncertainty relations in terms of the Renyi entropies [J].

Bialynicki-Birula, Iwo .

PHYSICAL REVIEW A, 2006, 74 (05)

[4] UNCERTAINTY RELATIONS FOR INFORMATION ENTROPY IN WAVE MECHANICS [J].

BIALYNICKIBIRULA, I ;

MYCIELSKI, J .

COMMUNICATIONS IN MATHEMATICAL PHYSICS, 1975, 44 (02) :129-132

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

Busch, Paul ;

Heinonen, Teiko ;

Lahti, Pekka .

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

[6] Improved bounds on entropic uncertainty relations [J].

de Vicente, Julio I. ;

Sanchez-Ruiz, Jorge .

PHYSICAL REVIEW A, 2008, 77 (04)

[7] UNCERTAINTY IN QUANTUM MEASUREMENTS [J].

DEUTSCH, D .

PHYSICAL REVIEW LETTERS, 1983, 50 (09) :631-633

[8] Certainty relations between local and nonlocal observables -: art. no. 256 [J].

Diaz, RG ;

Romero, JL ;

Björk, G ;

Bourennane, M .

NEW JOURNAL OF PHYSICS, 2005, 7 :1-10

[9] OVERLAP AND DISTINGUISHABILITY OF QUANTUM STATES [J].

DIEKS, D .

PHYSICS LETTERS A, 1988, 126 (5-6) :303-306

[10] Quantum Covariance, Quantum Fisher Information, and the Uncertainty Relations [J].

Gibilisco, Paolo ;

Hiai, Fumio ;

Petz, Denes .

IEEE TRANSACTIONS ON INFORMATION THEORY, 2009, 55 (01) :439-443

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