A modified frequency domain condition for the physical realizability of linear quantum stochastic systems

Arash Kh Sichani; Ian R. Petersen

doi:10.1109/TAC.2017.2726340

A modified frequency domain condition for the physical realizability of linear quantum stochastic systems

Arash Kh Sichani^*, Ian R. Petersen

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

7 Citations (Scopus)

Abstract

This paper is concerned with a modified version of the frequency domain physical realizability (PR) condition for linear quantum systems. We consider open quantum systems whose dynamic variables satisfy the canonical commutation relations of an open quantum harmonic oscillator and are governed by linear quantum stochastic differential equations (QSDEs). In order to correspond to physical quantum systems, these QSDEs must satisfy PR conditions.We provide a relatively simple proof that the PR condition is equivalent to the frequency domain (J, J)-unitarity of the input-output transfer function and orthogonality of the feedthrough matrix of the system without the technical spectral assumptions required in previous work. We also show that the poles and transmission zeros associated with the transfer function of PR linear quantum systems are the mirror reflections of each other about the imaginary axis. An example is provided to illustrate the results.

Original language	English
Pages (from-to)	277-282
Number of pages	6
Journal	IEEE Transactions on Automatic Control
Volume	63
Issue number	1
DOIs	https://doi.org/10.1109/TAC.2017.2726340
Publication status	Published - Jan 2018

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abstract = "This paper is concerned with a modified version of the frequency domain physical realizability (PR) condition for linear quantum systems. We consider open quantum systems whose dynamic variables satisfy the canonical commutation relations of an open quantum harmonic oscillator and are governed by linear quantum stochastic differential equations (QSDEs). In order to correspond to physical quantum systems, these QSDEs must satisfy PR conditions.We provide a relatively simple proof that the PR condition is equivalent to the frequency domain (J, J)-unitarity of the input-output transfer function and orthogonality of the feedthrough matrix of the system without the technical spectral assumptions required in previous work. We also show that the poles and transmission zeros associated with the transfer function of PR linear quantum systems are the mirror reflections of each other about the imaginary axis. An example is provided to illustrate the results.",

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AB - This paper is concerned with a modified version of the frequency domain physical realizability (PR) condition for linear quantum systems. We consider open quantum systems whose dynamic variables satisfy the canonical commutation relations of an open quantum harmonic oscillator and are governed by linear quantum stochastic differential equations (QSDEs). In order to correspond to physical quantum systems, these QSDEs must satisfy PR conditions.We provide a relatively simple proof that the PR condition is equivalent to the frequency domain (J, J)-unitarity of the input-output transfer function and orthogonality of the feedthrough matrix of the system without the technical spectral assumptions required in previous work. We also show that the poles and transmission zeros associated with the transfer function of PR linear quantum systems are the mirror reflections of each other about the imaginary axis. An example is provided to illustrate the results.

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A modified frequency domain condition for the physical realizability of linear quantum stochastic systems

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