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IEEE Transactions on Automatic Control

Two-Disk Synthesis of Coherent Quantum Passive Equalizers for Channels With Hamiltonian Uncertainty

Shuixin Xiao, Weichao Liang, Daoyi Dong, Ian R. Petersen, Valery Ugrinovskii

Published Feb 2, 2026• 0 citations
Publisher

Abstract

The coherent equalization problem involves designing a quantum system that serves as a mean-square near-optimal filter for a given quantum communication channel. Previous work on coherent equalization has typically assumed that the system parameters are known without uncertainty. In this work, we address the problem of coherent passive equalization with uncertainty in the Hamiltonian. Utilizing an S-procedure method, we remodel the passive quantum system with uncertainty as a scaled closed-loop state-space representation with parameter dependencies. We then propose a two-disk synthesis approach for coherent passive equalizers. Numerical examples based on a single optical cavity system and on two-cavity systems with beam splitters demonstrate the effectiveness of the proposed two-disk synthesis method for coherent equalization of passive quantum systems.

DOI
10.1109/tac.2026.3660081

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The coherent equalization problem involves designing a quantum system that serves as a mean-square near-optimal filter for a given quantum communication channel. Previous work on coherent equalization has typically assumed that the system parameters are known without uncertainty. In this work, we address the problem of coherent passive equalization with uncertainty in the Hamiltonian. Utilizing an S-procedure method, we remodel the passive quantum system with uncertainty as a scaled closed-loop state-space representation with parameter dependencies. We then propose a two-disk synthesis approach for coherent passive equalizers. Numerical examples based on a single optical cavity system and on two-cavity systems with beam splitters demonstrate the effectiveness of the proposed two-disk synthesis method for coherent equalization of passive quantum systems.
The coherent equalization problem consists in designing a quantum system acting as a mean-square near-optimal filter for a given quantum communication channel. The paper develops an improved method for the synthesis of transfer functions for such equalizing filters, based on a linear quantum system model of the channel. The method draws on a connection with the two-disk problem of H ∞ control for classical (i.e., non-quantum) linear uncertain systems. Compared with the previous methods, the proposed method applies to a broader class of linear quantum communication channels.
The paper considers the problem of equalization of passive linear quantum systems. While our previous work was concerned with the analysis and synthesis of passive equalizers, in this paper we analyze coherent quantum equalizers whose annihilation (respectively, creation) operator dynamics in the Heisenberg picture are driven by both quadratures of the channel output field. We show that the characteristics of the input field must be taken into consideration when choosing the type of the equalizing filter. In particular, we show that for thermal fields allowing the filter to process both quadratures of the channel output may not improve mean square accuracy of the input field estimate, in comparison with passive filters. This situation changes when the input field is `squeezed'.
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Coherent feedback H∞H^\inftyH∞ control of quantum linear systems
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