Trapped Modes in Linear Quantum Stochastic Networks with Delays

TL;DR

This paper introduces a systematic method to identify trapped modes in linear quantum networks with feedback and delays, extending existing quantum network modeling techniques to include finite propagation times.

Contribution

It applies the Blaschke-Potapov factorization theorem to quantum networks, enabling automated detection of trapped modes caused by feedback delays.

Findings

Provides a new methodology for trapped mode identification

Extends quantum network modeling to include delays

Facilitates automated quantum network analysis

Abstract

Networks of open quantum systems with feedback have become an active area of research for applications such as quantum control, quantum communication and coherent information processing. A canonical formalism for the interconnection of open quantum systems using quantum stochastic differential equations (QSDEs) has been developed by Gough, James and co-workers and has been used to develop practical modeling approaches for complex quantum optical, microwave and optomechanical circuits/networks. In this paper we fill a significant gap in existing methodology by showing how trapped modes resulting from feedback via coupled channels with finite propagation delays can be identified systematically in a given passive linear network. Our method is based on the Blaschke-Potapov multiplicative factorization theorem for inner matrix-valued functions, which has been applied in the past to analog electronic networks. Our results provide a basis for extending the Quantum Hardware Description Language (QHDL) framework for automated quantum network model construction (Tezak \textit{et al.} in Philos. Trans. R. Soc. A, Math. Phys. Eng. Sci. 370(1979):5270-5290, to efficiently treat scenarios in which each interconnection of components has an associated signal propagation time delay.