迹范数中的Birkhoff-James正交，及其在量子资源理论中的应用

IF 0.7 4区数学 Q2 Mathematics

Electronic Journal of Linear Algebra Pub Date : 2021-09-12 DOI:10.13001/ela.2022.7149

N. Johnston, Shirin Moein, Rajesh Pereira, S. Plosker

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引用次数: 1

摘要

在迹范数上，给出了复数厄米矩阵与(厄米)正半定矩阵或正半定矩阵集的birkhof - james正交的许多结果。例如，在迹范数中，给出了判定哪些厄米矩阵与所有正半定对角矩阵的集合是Birkhoff-James正交的一个简单检验准则。探讨了量子资源理论中的应用。例如，描述了相干修正迹距离等于$1$(最大可能值)的量子态，并建立了$2$-纠缠修正迹距离与NPPT束缚纠缠问题之间的联系。

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Birkhoff-James orthogonality in the trace norm, with applications to quantum resource theories

Numerous results are presented that characterize when a complex Hermitian matrix is Birkhoff-James orthogonal, in the trace norm, to a (Hermitian) positive semidefinite matrix or set of positive semidefinite matrices. For example, a simple-to-test criterion that determines which Hermitian matrices are Birkhoff-James orthogonal, in the trace norm, to the set of all positive semidefinite diagonal matrices is developed. Applications in the theory of quantum resources are explored. For example, the quantum states that have modified trace distance of coherence equal to $1$ (the maximal possible value) are characterized, and a connection between the modified trace distance of $2$-entanglement and the NPPT bound entanglement problem is established.

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来源期刊

Electronic Journal of Linear Algebra 数学-数学

CiteScore

1.20

自引率

14.30%

发文量

审稿时长

6-12 weeks

期刊介绍： The journal is essentially unlimited by size. Therefore, we have no restrictions on length of articles. Articles are submitted electronically. Refereeing of articles is conventional and of high standards. Posting of articles is immediate following acceptance, processing and final production approval.