非 $$H_2$$ 可简矩阵和一些特殊的复哈达玛矩阵

IF 2.2 3区物理与天体物理 Q1 PHYSICS, MATHEMATICAL Quantum Information Processing Pub Date : 2024-07-19 DOI:10.1007/s11128-024-04482-y

Mengfan Liang, Lin Chen, Fengyue Long, Xinyu Qiu

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引用次数: 0

摘要

描述复哈达玛矩阵（CHMs）是线性代数和量子信息领域的一个开放性问题。我们将除$H_2$可简矩阵和Tao矩阵之外的$6\times 6) CHMs命名为非\(H_2$可简矩阵。据我们所知，还没有发现具有解析形式的非（H_2\）-可简化矩阵。在本文中，我们发现了一些具有解析形式的非（H_2\）可简化矩阵。我们还描述了一些特殊的 $6\times 6$ CHM。利用我们的结果，我们可以进一步缩小 MUB 三元组的范围（在 $\mathbb {C}^6$ 中，四个 MUB 的集合包括一个 MUB 三元组和同一性）。我们的结果可能会导致对 $6\times 6$ CHM 的完整分类，并解决 $\mathbb {C}^6$ 中的 MUB 问题。

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The non-$H_2$-reducible matrices and some special complex Hadamard matrices

Characterizing the $6\times 6$ complex Hadamard matrices (CHMs) is an open problem in linear algebra and quantum information. We name the $6\times 6$ CHMs except the $H_2$-reducible matrices and the Tao matrix as the non-$H_2$-reducible matrices. As far as we know, no non-$H_2$-reducible matrices with analytic form have been found. In this paper, we find some non-$H_2$-reducible matrices with analytic form. We also characterize some special $6\times 6$ CHMs. Using our result one can further narrow the range of MUB trio (a set of four MUBs in $\mathbb {C}^6$ consists of an MUB trio and the identity). Our results may lead to the complete classification of $6\times 6$ CHMs and the solution of MUB problem in $\mathbb {C}^6$.

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来源期刊

Quantum Information Processing 物理-物理：数学物理

CiteScore

4.10

自引率

20.00%

发文量

337

审稿时长

4.5 months

期刊介绍： Quantum Information Processing is a high-impact, international journal publishing cutting-edge experimental and theoretical research in all areas of Quantum Information Science. Topics of interest include quantum cryptography and communications, entanglement and discord, quantum algorithms, quantum error correction and fault tolerance, quantum computer science, quantum imaging and sensing, and experimental platforms for quantum information. Quantum Information Processing supports and inspires research by providing a comprehensive peer review process, and broadcasting high quality results in a range of formats. These include original papers, letters, broadly focused perspectives, comprehensive review articles, book reviews, and special topical issues. The journal is particularly interested in papers detailing and demonstrating quantum information protocols for cryptography, communications, computation, and sensing.

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