论文标题
在某些单一合奏中的随机矩阵中的内在块上
On the immanants of blocks from random matrices in some unitary ensembles
论文作者
论文摘要
由于与Hong-Ou-Mandel效应和玻色子采样问题的联系，统一矩阵及其块的永久性引起了人们对量子物理和量子计算的越来越多的关注。在这种情况下，了解随机矩阵的永久性或其他内在物的分布将是有用的，但这似乎是一个困难的问题。我们通过计算统一组中随机矩阵的宽度块的平方模量的平均值，在正交组和圆形正式正交中的平均值。对于统一组的永久性，我们还计算了差异。我们的方法基于Weingarten功能和排列的因素化。在计算过程中，我们被导致猜想与正交组的不可还原表示的尺寸与身份划分多项式的值相关。
The permanent of unitary matrices and their blocks has attracted increasing attention in quantum physics and quantum computation because of connections with the Hong-Ou-Mandel effect and the Boson Sampling problem. In that context, it would be useful to know the distribution of the permanent or other immanants for random matrices, but that seems a difficult problem.We advance this program by calculating the average of the squared modulus of a generic immanant for blocks from random matrices in the unitary group, in the orthogonal group and in the circular orthogonal ensemble. In the case of the permanent in the unitary group, we also compute the variance. Our approach is based on Weingarten functions and factorizations of permutations. In the course of our calculations we are led to a conjecture relating dimensions of irreducible representations of the orthogonal group to the value of zonal polynomials at the identity.
