EPJ Quantum Technol. (2016) 3: 3
https://doi.org/10.1140/epjqt/s40507-016-0041-9

Research

Trapped modes in linear quantum stochastic networks with delays

¹ Department of Applied Physics, Stanford University, 348 Via Pueblo Mall, Stanford, CA, 94305, USA

^* e-mail: tabakg@stanford.edu

Received: 26 October 2015
Accepted: 22 February 2016
Published online: 3 March 2016

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 et al. in Philos. Trans. R. Soc. A, Math. Phys. Eng. Sci. 370(1979):5270-5290, 2012) to efficiently treat scenarios in which each interconnection of components has an associated signal propagation time delay.