本文為描述量子力學系統奠定了數學基礎，並探討量子資訊理論中的核心問題。本研究以量子力學、線性代數、機率論及經典資訊理論的公理為基礎，運用 Naimark 的擴張定理、Schmidt 分解及 Holevo 界限等數學工具。參考 Holevo、Bennett 等學者的基礎文獻，系統性地探究了經典-量子通路的編碼定理。具體而言，本研究探討發送者與接收者之間預先共享的糾纏現象，如何影響加性問題，並闡明量子通道上經典通訊容量的極限。;This thesis establishes a mathematical foundation for describing quantum mechanical systems and explores core problems within quantum information theory. Grounded in the axioms of quantum mechanics， linear algebra， probability theory， and classical information theory， this work utilizes mathematical tools such as Naimark′s dilation theorem， Schmidt decomposition， and the Holevo bound. Drawing upon foundational literature by Holevo， Bennett， and others， we systematically investigate the coding theorems of classical-quantum channels. Specifically， this study examines how the presence of pre-shared entanglement between the sender and receiver impacts the additivity problem and characterizes the limits of classical communication capacity over quantum channels.
