论文标题
通过Weingarten演算的随机量子边缘的矩
Moments of random quantum marginals via Weingarten calculus
论文作者
论文摘要
随机量子边缘问题询问了均匀的随机Hermitian操作员的部分迹线（“边缘”）的联合分布，其固定光谱作用于张量的空间。我们基于研究边际条目的混合时刻引入了一种新的方法。对于描述可区分颗粒，玻色子或费米的系统的随机量子边缘问题，我们证明了这些混合力矩的公式，这些矩完全确定了边际分布。我们的主要工具是Weingarten演算，它提供了一种计算多项式函数积分的方法，相对于单一组上的HAAR度量。作为一种应用，在两个可区分的粒子的情况下，我们证明了边缘渐近行为的一些结果，因为一个或两个希尔伯特空间的尺寸是无穷大的。
The randomized quantum marginal problem asks about the joint distribution of the partial traces ("marginals") of a uniform random Hermitian operator with fixed spectrum acting on a space of tensors. We introduce a new approach to this problem based on studying the mixed moments of the entries of the marginals. For randomized quantum marginal problems that describe systems of distinguishable particles, bosons, or fermions, we prove formulae for these mixed moments, which determine the joint distribution of the marginals completely. Our main tool is Weingarten calculus, which provides a method for computing integrals of polynomial functions with respect to Haar measure on the unitary group. As an application, in the case of two distinguishable particles, we prove some results on the asymptotic behavior of the marginals as the dimension of one or both Hilbert spaces goes to infinity.
