交换代数的拟正交性，复哈达玛矩阵和互无偏测量

IF 1.1 3区数学 Q1 MATHEMATICS

Linear Algebra and its Applications Pub Date : 2025-09-16 DOI:10.1016/j.laa.2025.09.010

Sooyeong Kim , David Kribs , Edison Lozano , Rajesh Pereira , Sarah Plosker

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引用次数: 0

摘要

通过对交换代数情况的分析，加深了拟正交和近似拟正交算子代数的理论。基于一个与复Hadamard矩阵有关的矩阵理论概念，给出了一种计算两个这样的矩阵子代数间正交测度的新方法。我们还展示了这个新工具如何产生关于一般非交换情况的重要信息。最后，我们考虑了量子信息论中由互无偏基和互无偏测量产生的交换代数的重要子类的拟正交性。我们在整个工作中提供了一些例子，包括一个由群代数和拉丁平方产生的子类。

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Quasiorthogonality of commutative algebras, complex Hadamard matrices, and mutually unbiased measurements

We deepen the theory of quasiorthogonal and approximately quasiorthogonal operator algebras through an analysis of the commutative algebra case. We give a new approach to calculate the measure of orthogonality between two such subalgebras of matrices, based on a matrix-theoretic notion we introduce that has a connection to complex Hadamard matrices. We also show how this new tool can yield significant information on the general non-commutative case. We finish by considering quasiorthogonality for the important subclass of commutative algebras that arise from mutually unbiased bases (MUBs) and mutually unbiased measurements (MUMs) in quantum information theory. We present a number of examples throughout the work, including a subclass that arises from group algebras and Latin squares.

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来源期刊

Linear Algebra and its Applications 数学-应用数学

CiteScore

2.20

自引率

9.10%

发文量

333

审稿时长

13.8 months

期刊介绍： Linear Algebra and its Applications publishes articles that contribute new information or new insights to matrix theory and finite dimensional linear algebra in their algebraic, arithmetic, combinatorial, geometric, or numerical aspects. It also publishes articles that give significant applications of matrix theory or linear algebra to other branches of mathematics and to other sciences. Articles that provide new information or perspectives on the historical development of matrix theory and linear algebra are also welcome. Expository articles which can serve as an introduction to a subject for workers in related areas and which bring one to the frontiers of research are encouraged. Reviews of books are published occasionally as are conference reports that provide an historical record of major meetings on matrix theory and linear algebra.