本論文提出了一個新的、對系統可分性充分必要的評判準則，而這個準則適用於任意有限維的純態雙分系統。並且我們也討論了與之對應的、對糾纏更精細的量化和描述(而不僅僅是作為糾纏與否的判斷)。基於這個評判準則，我們證明了著名的Peres-Horodecki positivity-of-partial-transform評判準則對純態雙分系統的可分性也是充分必要的。最後我們推導出了糾纏的最大值，並且也詳盡地給出了相應的最大糾纏態。

A new criterion necessary and sufficient for the separability of pure bipartite systems for arbitrary finite dimensions is demonstrated; and the corresponding finer quantitative measures or characterizations of entanglement (beyond mere separability or nonseparability determination) are discussed. Based on this criterion, we proved that the well-known Peres-Horodecki positivity-of-partial-transform criterion is also necessary and sufficient for separability in the case of pure bipartite systems. The maximum value of entanglement, and the corresponding maximally-entangled states are also worked out in detail.

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