Derivation of the Loop Hafnian Generating Function for Arbitrary Symmetric Matrices via Gaussian Integration

Abstract

This short note shows that the recently proposed generating function for loop hafnians -- originally derived using quantum-optical methods for a restricted class of matrices -- is in fact valid for arbitrary symmetric matrices. The proof relies solely on Gaussian integration and does not assume any additional properties inherited from the covariance matrices of quantum Gaussian states.

arXiv comment5 pages