POSITIVE OPERATOR-VALUED MEASURES AND DENSELY DEFINED OPERATOR-VALUED FRAMES

被引：1

作者：

Robinson, Benjamin ^{[1
]}

Moran, Bill ^{[2
]}

Cochran, Doug ^{[3
]}

机构：

[1] US Air Force Res Lab, 2241 Av Cir, Wright Patterson AFB, OH 45433 USA

[2] Univ Melbourne, Dept Elect & Elect Engn, Parkville, Vic 3010, Australia

[3] Arizona State Univ, Sch Math & Stat Sci, Tempe, AZ 85287 USA

来源：

ROCKY MOUNTAIN JOURNAL OF MATHEMATICS | 2021年 / 51卷 / 01期

关键词：

frames; g-frames; operator-valued frames; positive operator-valued measures; Radon-Nikodym theorem;

D O I：

10.1216/rmj.2021.51.265

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In the signal-processing literature, a frame is a mechanism for performing analysis and reconstruction in a Hilbert space. By contrast, in quantum theory, a positive operator-valued measure (POVM) decomposes a Hilbert-space vector for the purpose of computing measurement probabilities. Frames and their most common generalizations can be seen to give rise to POVMs, but does every reasonable POVM arise from a type of frame? We answer this question using a Radon-Nikodym-type result.

引用

页码：265 / 272

页数：8

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