Yen-Chi Lee's Academic Website

Short Bio

I am an Assistant Professor in the Department of Mathematics at National Central University (NCU), with a joint appointment in the Department of Communication Engineering. I lead the Information Theory and Applied Probability (ITAP) Lab. Before joining NCU, I was an Assistant Research Fellow at the Quantum Computing Research Center, Hon Hai Research Institute, from 2021 to 2024.

I received my Ph.D. from the Graduate Institute of Communication Engineering (GICE), National Taiwan University (NTU), where I also earned my M.S. in Mathematics and B.S. in Electrical Engineering (NTUEE).

My research connects stochastic processes, information theory, and quantum theory. I study how transport mechanisms, boundary geometry, and symmetry shape the mathematical structure and information limits of classical and quantum channels. Current topics include first-hitting distributions, diffusion-based molecular communication, non-Gaussian channels, and the capacities of symmetric quantum channels.

Research Interests

My work brings together applied probability, stochastic analysis, information theory, and operator methods. I am particularly interested in how the structure of a physical model determines the probability laws or quantum maps governing information transmission.

A. Stochastic Transport and Boundary Observables

I study stochastic transport through the times and locations at which a process first reaches a boundary. Using diffusion generators, Green functions, boundary-value problems, and change-of-measure techniques, I analyze how drift, geometry, and absorbing boundaries determine these hitting laws.

Recent topics include joint arrival-time and arrival-position distributions, exact channel impulse responses for spherical receivers, and first-passage models with time-dependent drift. Diffusion-based molecular communication provides a concrete setting in which these mathematical structures lead to observable channel behavior.

B. Non-Gaussian Channels and Information Limits

I investigate communication channels whose noise laws arise from stochastic transport and boundary-hitting mechanisms. These laws can exhibit Cauchy-type behavior, Gaussian variance-mixture structure, and transitions between heavy-tailed and exponentially decaying regimes.

My work examines how these features affect channel capacity, optimal signaling, detection, and estimation. Current directions include capacity scaling laws, signal detection under heavy-tailed noise, spatial reception and aperture selection, and timing channels under pulsatile drift. A central goal is to connect analytical channel models with precise statements about information transmission.

C. Symmetric Quantum Channels and Mathematical Foundations

I study how symmetry and operator structure constrain quantum noise and quantum channel capacities. My current work focuses on approximate degradability, constructive degrading maps, diamond-norm estimates, and capacity bounds in the low-noise regime.

Using matrix analysis, functional analysis, and representation theory, I investigate symmetric channel families, including Landau–Streater channels and channels generated by Lie-algebra representations. This direction connects the mathematical foundations of quantum theory with quantitative questions about quantum communication.

簡歷

我目前擔任國立中央大學數學系助理教授，並合聘於通訊工程學系，主持「資訊理論與應用機率實驗室」（Information Theory and Applied Probability Lab，ITAP Lab）。加入中央大學之前，我於 2021 至 2024 年任職於鴻海研究院量子計算研究中心，擔任助理研究員。

我在國立臺灣大學電信工程學研究所取得博士學位，並於同校取得數學碩士與電機工程學士學位。這些跨領域訓練，構成我結合機率、分析、通訊與量子理論的研究基礎。

我的研究以隨機過程、資訊理論與量子理論為核心，探討隨機輸運、邊界幾何與對稱性如何決定古典及量子通道的結構與資訊極限。目前主要研究首次擊中分布、擴散式分子通訊、非高斯通道，以及對稱量子通道的容量問題。

研究領域

我的研究結合應用機率、隨機分析、資訊理論與算子方法，關注物理模型的結構如何決定資訊傳輸所依循的機率分布或量子映射，並進一步影響偵測、估測與通道容量。

一、隨機輸運與邊界可觀測量

我透過隨機過程首次到達邊界的時間、位置及其聯合分布，研究隨機輸運的行為。主要方法包含擴散生成算子、Green 函數、邊界值問題與測度轉換，用以分析漂移、幾何形狀及吸收邊界對擊中分布的影響。

近期主題包括到達時間與位置的聯合統計、球形接收器的精確通道脈衝響應，以及時變漂移下的首次通過問題。擴散式分子通訊是其中的重要應用，也提供了連結隨機模型、邊界觀測與通道行為的具體場景。

二、非高斯通道與資訊極限

我研究由隨機輸運與邊界擊中機制所誘導的通道模型。這類模型可能呈現 Cauchy 型雜訊、高斯變異數混合結構，以及由重尾衰減轉為指數衰減的現象。

我關注這些分布特徵如何影響通道容量、最佳訊號設計、偵測與估測。目前的研究方向包含容量尺度律、重尾雜訊下的訊號偵測、空間接收與孔徑選擇，以及脈動漂移下的計時通道。核心目標是從可分析的通道模型出發，建立關於資訊傳輸能力的精確描述。

三、對稱量子通道與數學基礎

我研究對稱性與算子結構如何限制量子雜訊及量子通道容量。目前主要關注近似可降解性、可建構的降解映射、diamond norm 估計，以及低雜訊區域的容量界。

研究方法包含矩陣分析、泛函分析與表示論，考察的對象包括 Landau–Streater 通道，以及由 Lie 代數表示所生成的量子通道族。此方向結合量子理論的數學基礎與量子通訊中的定量問題。

Student Research Projects and Reading Groups

專題研究與讀書會

ITAP Lab 歡迎對隨機過程、資訊理論或量子理論有興趣的大學部與研究所同學洽詢。研究與閱讀方向可依背景調整，從教材閱讀、數學推導與數值實驗開始，逐步發展為專題研究、畢業專題或研究計畫。

一、應用機率、資訊理論與通訊模型

適合對隨機過程、通道建模、資訊理論、偵測與估測或數值模擬有興趣的同學。可能主題包括擴散與首次擊中問題、分子通訊、非高斯雜訊、通道容量，以及 MATLAB／Python 數值驗證。可依背景從基本機率模型或小型模擬專題開始。

二、量子資訊與數學物理

適合對量子理論、量子通道或其數學架構有興趣的同學。閱讀與研究主題包括 Hilbert 空間、量子態與測量、算子與譜理論、量子通道、量子熵及群表示論。可從線性代數與入門量子資訊教材出發，逐步銜接通道結構與容量問題。

三、數學分析讀書會

適合希望強化分析基礎，或準備進入機率、偏微分方程與量子理論研究的同學。主題可包含實分析、測度與積分、Fourier 分析及泛函分析，依參與者程度選擇教材與進度，重視定義、證明與具體例子之間的連結。

參與準備與聯絡方式

建議具備微積分、線性代數與基礎機率；進階工具可隨題目逐步學習。我重視清楚的問題意識、嚴謹推導與可重現的數值驗證，也歡迎尚未確定研究方向、希望先從閱讀開始的同學。

有興趣者請寄信至 yclee@math.ncu.edu.tw，附上簡短自我介紹、相關修課紀錄，以及希望探索的方向。