Design of Coherent Passive Quantum Equalizers Using Robust Control Theory

Core Concepts

Developing coherent equalizing filters for quantum communication channels using robust control theory.

Abstract

The content introduces a methodology for designing coherent equalizing filters for quantum communication channels. It discusses the challenges faced in quantum communication due to environmental effects and channel distortions, proposing a systematic algorithm for filter synthesis. The paper explores the analogy with classical communication channels and addresses the optimization problem of mean-square mismatch between input and output fields. It delves into passive quantum systems, spectral factorization, and semidefinite programming for filter design.

Stats

The main result is a systematic equalizer synthesis algorithm. The task involves equalization of classical communication channels. The transfer function G(s) relates bilateral Laplace transforms of y(t), d(t), u(t), w(t). A coherent filter optimizes the power spectrum density (PSD) of the difference between field u and filter output field ˆu. The system must be stable, causal, and paraunitary.

Quotes

"The aim is to obtain a filtering device which minimizes the mismatch between u and ˆu in the mean-square sense." "Coherent equalization seeks to mitigate environmental and channel distortions blue in the system by coupling it with another quantum physical system acting as a filter." "The proposed relaxation has two significant features."

Key Insights Distilled From

Design of Coherent Passive Quantum Equalizers Using Robust Control Theory

by V. Ugrinovsk... at arxiv.org 03-20-2024

https://arxiv.org/pdf/2308.15805.pdf

Deeper Inquiries

How can the findings on coherent equalization in quantum systems be applied to real-world quantum communication technologies

The findings on coherent equalization in quantum systems can be applied to real-world quantum communication technologies by improving the efficiency and reliability of quantum communication channels. By designing coherent equalizers using robust control theory, it is possible to mitigate environmental effects and channel distortions that degrade the quality of transmitted information in quantum communication systems. This can lead to enhanced signal-to-noise ratios, reduced errors, and improved overall performance of quantum communication channels. Implementing these coherent passive quantum equalizers can help optimize the transmission of quantum information over long distances with minimal loss or distortion.

What are potential drawbacks or limitations of using completely passive quantum systems for coherent equalization

One potential drawback of using completely passive quantum systems for coherent equalization is the limited flexibility in adjusting system parameters once they are implemented. Since passive systems rely on fixed configurations of optical components like beam splitters and phase shifters, there may be constraints on adaptability or scalability as operational requirements change over time. Additionally, completely passive systems may have inherent limitations in terms of complexity and computational capabilities compared to active systems that involve external sources for manipulation.

How does the concept of spectral factorization impact the design and implementation of coherent passive quantum equalizers

The concept of spectral factorization plays a crucial role in the design and implementation of coherent passive quantum equalizers by ensuring stability and causality while meeting physical realizability constraints. Spectral factorization allows for decomposing complex transfer functions into simpler components that facilitate analysis and optimization processes. By satisfying Assumption 1 related to spectral factorization, designers can ensure that physically realizable solutions exist for constructing near-optimal filters with guaranteed performance bounds. This approach enables systematic synthesis methods based on semidefinite programming techniques, leading to efficient designs for coherent passive equalizing filters in linear quantum systems.