A generalized approach to quantum interference in lossy N-port devices via a singular value decomposition

TL;DR

This paper introduces a singular value decomposition method to efficiently model quantum interference in lossy N-port devices, enabling better understanding and design of complex quantum optical systems with dissipation.

Contribution

It presents a novel SVD-based procedure for deriving input-output relations in arbitrary lossy linear quantum devices, addressing a key theoretical challenge.

Findings

Effective calculation of input-output relations for lossy devices

Application to reciprocal and nonreciprocal devices with complex scattering matrices

Provides an intuitive understanding of device operation principles

Abstract

Modeling quantum interference in the presence of dissipation is a critical aspect of quantum technologies. Including dissipation into the model of a linear device enables for assesing the detrimental impact of photon loss, as well as for studying dissipation-driven quantum state transformations. However, establishing the input-output relations characterizing quantum interference at a general lossy N-port network poses important theoretical challenges. Here, we propose a general procedure based on the singular value decomposition (SVD), which allows for the efficient calculation of the input-output relations for any arbitrary lossy linear device. In addition, we show how the SVD provides an intuitive description of the principle of operation of linear optical devices. We illustrate the applicability of our method by evaluating the input-output relations of popular reciprocal and nonreciprocal lossy linear devices, including devices with singular and nilpotent scattering matrices. We expect that our procedure will motivate future research on quantum interference in complex devices, as well as the realistic modelling of photon loss in linear lossy devices.