Year: 2025
Type: article
Abstract: Products of truncated unitary matrices, independently and uniformly drawn from the unitary group, can be used to study universal aspects of monitored quantum circuits. The von Neumann entropy of the corresponding density matrix decreases with increasing the length L of the product chain, in a way that depends on the matrix dimension N and the truncation depth δN. Here we study that dependence in the double-scaling limit L,N→∞ at the fixed ratio τ=LδN/N. The entropy reduction crosses over from a linear to a logarithmic dependence on τ when this parameter crosses unity. The central technical result is an expression for the singular-value moments of the matrix product in terms of the Erlang function from queueing theory.
Source: Physical review. E
Author: C. W. J. Beenakker
Institution: Leiden University
Language: English
Topic: Quantum many-body systems
Subfield: Atomic and Molecular Physics, and Optics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4406733914