吾人提出了雙量子位元純態之糾纏最重要的理論以及數學性質的回顧及解析。在簡明地敘述了希爾伯特空間的幾何之後；藉由詮釋雙量子位元純態之幾何以及透過奇異值分解與施密特數的研究，吾人推導出描述雙量子位元純態之糾纏的測度。對雙量子位元系統而言，該測度於幾何上我們可以視其為S^7/[S^3⨂S^3 ]的結構。吾人據此推導出的雙量子位元純態之糾纏測度被證明與許多著名的糾纏測度同調；例如約化密度矩陣的von Neumann entropy，CHSH算符之最大期望值，以及Wooter的concurrence。接著吾人給出針對糾纏測度之時間演化的完整描述，並且完整討論了糾纏測度於Schro ̈dinger演化下的充分與必要條件，並且附上兩個有意義的範例作為說明。而Anandan-Aharonov 相位也被證明與雙量子位元純態之糾纏無關。

An analysis and review of the most important theoretical and mathematical properties of pure bipartite qubit-qubit entanglement is presented. After a short description of the geometry of Hilbert spaces, the entanglement measure is derived, both from a geometrical perspective and also by singular value decomposition and Schmidt number analysis. For bipartite qubit-qubit systems, the entanglement can be identified with the quotient space $[S^{7}/S^{3}otimes S^3]$. The measure of entanglement derived is shown to be monotonic to various other well-known entanglement parameters such as the von Neumann entropy of the reduced density matrix, maximum of the expectation value of Clauser-Horne-Shimony-Holt operator, and Wooters' concurrence. A complete description of the time evolution of the entanglement parameter is given. The necessary and sufficient condition for entanglement to be preserved under Schrodinger evolution is discussed, and illustrated explicitly with nontrivial examples. It is also confirmed that entanglement is independent of Abelian geometric phase or the Anandan-Aharonov phase.

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