研究生: |
黃哲緯 Huang, Che-Wei |
---|---|
論文名稱: |
量子混態訊號之可存取訊息量 Accessible Information for Quantum Mixed-state Signals |
指導教授: |
呂忠津
Lu, Chung-Chin |
口試委員: |
林茂昭
蘇育德 蘇賜麟 加藤研太郎 Kentaro Kato |
學位類別: |
碩士 Master |
系所名稱: |
電機資訊學院 - 電機工程學系 Department of Electrical Engineering |
論文出版年: | 2011 |
畢業學年度: | 99 |
語文別: | 中文 |
論文頁數: | 78 |
中文關鍵詞: | 量子混態訊號 、可存取訊息量 |
外文關鍵詞: | Quantum Mixed-state Signals, Accessible Information |
相關次數: | 點閱:1 下載:0 |
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可存取訊息量 (Accessible Information) 是一個量子通訊系統之安全性的評估因子,該訊息量被定義為: 給定一個訊號源 (Signal Source),針對量子測量最佳化可得到的最大互訊息量 (Maximum Mutual Information)。給定訊號源的情況下,互訊息 (Mutual Information) 對於測量是一凸函數,並且所有測量本身形成一凸集合 (Convex Set),因此上述之最佳化屬於凸集最大化 (Convex Maximization) 問題。目前這種最佳化問題並沒有一般解,但是,先前的研究者已經針對這個問題的子集合,例如針對某一類訊號源,提出一些結果。以往的研究者,幾乎都是以純態訊號 (Pure-state Signals) 為對象做研究,因為純態訊號比較容易處理。但是真實世界並不存在穩定的純態訊號。量子狀態在真實世界皆是以混態 (Mixed states) 的方式穩定存在。因此,對混態訊號的探討有其必要性。除了上述原因,混態訊號也是大多數量子通訊系統中,竊聽者所能獲取的訊號形式。如果能夠得知竊聽者所能獲得的最大互訊息量,那就多了一個層面分析量子通訊系統的安全性。
我們探討雙重對稱混態訊號 (Doubly Symmetric Mixed-state Signals, DSMS) 的可存取訊息量。雙重對稱混態訊號是竊聽者在αη類型的量子通訊系統中所能竊取到的訊號形式。我們證明一個軌道 (Orbit) 的量子測量就足夠達到可存取訊息量。除此之外,針對二元雙重對稱混態訊號 (Binary DSMS),我們計算出可存取訊息量的閉合形式解 (Closed-form Solution),並且我們發現分解平方根測量 (Decomposed Square-Root Measurement, DSRM) 是此可存取訊息量的最大化器 (Maximizer) 之一。根據附錄的計算,分解平方根測量和平方根測量 (Square-Root Measurement, SRM) 可以達到同樣的互訊息量。所以,平方根測量也是最大化器之一。
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