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

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

URL: http://arxiv.org/abs/2507.16100v1
Date: Mon, 21 Jul 2025 22:55:55 GMT
Title: Derivation of the Loop Hafnian Generating Function for Arbitrary Symmetric Matrices via Gaussian Integration
Authors: Sergey V. Tarasov,
Abstract summary: This note shows that the recently proposed generating function for loop hafnians is in fact valid for arbitrary symmetric matrices.<n>The proof relies solely on Gaussian integration and does not assume any additional properties inherited from the covariance matrices of quantum Gaussian states.
Score: 0.0
License: http://creativecommons.org/licenses/by/4.0/
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.

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