On the response of quantum linear systems to single photon input fields

TL;DR

This paper extends linear systems theory to quantum signals, characterizing how quantum linear systems respond to multichannel single photon inputs and defining a class of photon-Gaussian states that are preserved by these systems.

Contribution

It introduces the class of photon-Gaussian states and shows their preservation under quantum linear systems, with transfer function relations for output state determination.

Findings

Photon-Gaussian states are preserved by quantum linear systems.

Transfer functions determine the output states from input states.

Equations for output signal intensities are derived.

Abstract

The purpose of this paper is to extend linear systems and signals theory to include single photon quantum signals. We provide detailed results describing how quantum linear systems respond to multichannel single photon quantum signals. In particular, we characterize the class of states (which we call {\em photon-Gaussian} states) that result when multichannel photons are input to a quantum linear system. We show that this class of quantum states is preserved by quantum linear systems. Multichannel photon-Gaussian states are defined via the action of certain creation and annihilation operators on Gaussian states. Our results show how the output states are determined from the input states through a pair of transfer function relations. We also provide equations from which output signal intensities can be computed. Examples from quantum optics are provided to illustrate the results.