Answer to a question by A. Mandarino, T. Linowski and K. Zyczkowski

IF 0.6 4区数学 Q4 MATHEMATICS, APPLIED

Infinite Dimensional Analysis Quantum Probability and Related Topics Pub Date : 2021-10-14 DOI:10.1142/s0219025723500054

M. Popa

引用次数: 0

Abstract

A recent work by A. Mandarino, T. Linowski and K. \.{Z}yczkowski left open the following question. If $ \mu_N $ is a certain permutation of entries of a $ N^2 \times N^2 $ matrix ("mixing map") and $ U_N $ is a $ N^2 \times N^2 $ Haar unitary random matrix, then is the family $ U_N, U_N^{\mu_N}, ( U_N^2 )^{\mu_N}, \dots , ( U_N^m)^{\mu_N} $ asymptotically free? (here by $A^{ \mu}$ we understand the matrix resulted by permuting the entries of $ A $ according to the permutation $ \mu $). This paper presents some techniques for approaching such problems. In particular, one easy consequence of the main result is that the question above has an affirmative answer.

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回答a . Mandarino, T. Linowski和K. Zyczkowski的问题

A. Mandarino, T. Linowski和K. Życzkowski最近的一项研究留下了以下问题。如果$ \mu_N $是一个$ N^2 \times N^2 $矩阵(“混合映射”)的某个元素的排列，$ U_N $是一个$ N^2 \times N^2 $ Haar酉随机矩阵，那么族$ U_N, U_N^{\mu_N}, ( U_N^2 )^{\mu_N}, \dots , ( U_N^m)^{\mu_N} $是渐近自由的吗?(这里通过$A^{ \mu}$我们理解根据$ \mu $的排列对$ A $的条目进行排列所得到的矩阵)。本文提出了解决这类问题的一些技术。特别是，主要结果的一个简单结果是，上面的问题有一个肯定的答案。

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

Infinite Dimensional Analysis Quantum Probability and Related Topics 数学-统计学与概率论

CiteScore

1.50

自引率

11.10%

发文量

审稿时长

>12 weeks

期刊介绍： In the past few years the fields of infinite dimensional analysis and quantum probability have undergone increasingly significant developments and have found many new applications, in particular, to classical probability and to different branches of physics. The number of first-class papers in these fields has grown at the same rate. This is currently the only journal which is devoted to these fields. It constitutes an essential and central point of reference for the large number of mathematicians, mathematical physicists and other scientists who have been drawn into these areas. Both fields have strong interdisciplinary nature, with deep connection to, for example, classical probability, stochastic analysis, mathematical physics, operator algebras, irreversibility, ergodic theory and dynamical systems, quantum groups, classical and quantum stochastic geometry, quantum chaos, Dirichlet forms, harmonic analysis, quantum measurement, quantum computer, etc. The journal reflects this interdisciplinarity and welcomes high quality papers in all such related fields, particularly those which reveal connections with the main fields of this journal.