On positive operator-valued measures generated by a family of one-dimensional projectors

IF 1.2 3区数学 Q1 MATHEMATICS

Annals of Functional Analysis Pub Date : 2024-04-22 DOI:10.1007/s43034-024-00351-y

G. G. Amosov, A. D. Baranov, D. A. Kronberg

引用次数: 0

Abstract

We study positive operator-valued measures generated by projections on one-dimensional subspaces. A special attention is paid to the case in which subspaces are spanned by vectors forming a Riesz basis. It is shown that the measurement fulfilled by such measure is informationally complete for quantum states being a convex hull of projections on subspaces spanned by the system of biorthogonal vectors. We also discuss the properties of different quantum channels associated with a discrete measurement. Finally, we show that our measurement allows to introduce a quantum instrument taking values in the set of two points.

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论一维投影族生成的正算子值度量

我们研究由一维子空间上的投影产生的正算子值度量。我们特别关注了子空间被构成里兹基的向量所跨越的情况。研究表明，对于量子态来说，这种量度所满足的测量是信息完整的，量子态是双向向量系统所跨子空间上投影的凸壳。我们还讨论了与离散测量相关的不同量子通道的特性。最后，我们证明了我们的测量可以引入在两点集合中取值的量子仪器。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Annals of Functional Analysis MATHEMATICS, APPLIED-MATHEMATICS

CiteScore

2.00

自引率

10.00%

发文量

期刊介绍： Annals of Functional Analysis is published by Birkhäuser on behalf of the Tusi Mathematical Research Group. Ann. Funct. Anal. is a peer-reviewed electronic journal publishing papers of high standards with deep results, new ideas, profound impact, and significant implications in all areas of functional analysis and all modern related topics (e.g., operator theory). Ann. Funct. Anal. normally publishes original research papers numbering 18 or fewer pages in the journal’s style. Longer papers may be submitted to the Banach Journal of Mathematical Analysis or Advances in Operator Theory. Ann. Funct. Anal. presents the best paper award yearly. The award in the year n is given to the best paper published in the years n-1 and n-2. The referee committee consists of selected editors of the journal.