Generating Functions and Automatic Differentiation for Photon-Number-Resolved Simulations with Multimode Gaussian States

• URL: http://arxiv.org/abs/2209.05330v1
• Date: Mon, 12 Sep 2022 15:39:46 GMT
• Title: Generating Functions and Automatic Differentiation for Photon-Number-Resolved Simulations with Multimode Gaussian States
• Authors: Erik Fitzke, Florian Niederschuh, and Thomas Walther
• Abstract summary: A simple and versatile method to simulate the photon statistics of multimode Gaussian states is presented. The generating functions for the photon number distribution, cumulative probabilities, moments, and factorial moments of the photon statistics are derived. Numerical results are obtained by using the machine learning framework PyTorch for automatic differentiation.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: A simple and versatile method to simulate the photon statistics of multimode Gaussian states based on automatic differentiation of generating functions is presented. The generating functions for the photon number distribution, cumulative probabilities, moments, and factorial moments of the photon statistics are derived. Related expressions for multimode photon-added and photon-subtracted Gaussian states are presented. Numerical results are obtained by using the machine learning framework PyTorch for automatic differentiation. It is demonstrated that this approach is well suited for practical simulations of the photon statistics of quantum optical experiments in realistic scenarios with low photon numbers, in which various sources of imperfections have to be taken into account. As an example, the detection probabilities of a recent multipartite time-bin coding quantum key distribution setup are determined and compared with the corresponding experimental values.

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