Dynamical analysis of quantum linear systems driven by multi-channel multi-photon states

TL;DR

This paper analyzes the dynamics of quantum linear systems driven by complex multi-channel multi-photon states, including entangled states, deriving formulas for output intensities and states, with broad applicability in quantum information processing.

Contribution

It introduces a general framework for analyzing multi-channel multi-photon states with quantum correlations in quantum linear systems, extending beyond separable states.

Findings

Derived formulas for output field intensities and states.

Analyzed three types of multi-photon states with different photon-channel configurations.

Demonstrated results through illustrative examples.

Abstract

In this paper, we investigate the dynamics of quantum linear systems where the input signals are multi-channel multi-photon states, namely states determined by a definite number of photons superposed in multiple input channels. In contrast to most existing studies on separable input states in the literature, we allow the existence of quantum correlation (for example quantum entanglement) in these multi-channel multi-photon input states. Due to the prevalence of quantum correlations in the quantum regime, the results presented in this paper are very general. Moreover, the multi-channel multi-photon states studied here are reasonably mathematically tractable. Three types of multi-photon states are considered: 1) $m$ photons superposed among $m$ channels, 2) $N$ photons superposed among $m$ channels where $N\geq m$, and 3) $N$ photons superposed among $m$ channels where $N$ is an arbitrary positive integer. Formulae for intensities and states of output fields are derived. Examples are used to demonstrate the effectiveness of the results.