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

Sergey V. Tarasov

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arXiv · 2507.16100

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

Sergey V. Tarasov

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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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BibTeX RIS

Sergey V. Tarasov. 2025-07-21. Derivation of the Loop Hafnian Generating Function for Arbitrary Symmetric Matrices via Gaussian Integration. https://arxiv.org/abs/2507.16100

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