在本論文中，我們探討普遍的多體純量子態之子系統的以下特徵：這些子系統在何種情況下必定呈現糾纏？這些子系統所屬的整體量子態何時只會有一種可能？以及當他們已經糾纏時，何時能夠保證其他子系統也會是糾纏的？第三個現象又被稱作糾纏傳遞。若多體的子系統大小超過整體系統大小的一半，我們證明它在任意劃分下幾乎一定是糾纏的。因此，隨機產生的多體純量子態對於糾纏分發中的損失容忍度極高，可望應用於需要靈活協作的量子資訊協定。在某些局部維度下，與這些子系統相容的整體量子態僅有一種，即原始的純態本身。相較之下，在最簡單的貝爾情境中，我們發現端點三體無通訊關聯性大多不具備此唯一性。為了進一步理解相容性與唯一性之關係，我們推導了所有與給定的子系統相容的密度矩陣之間的關係。藉此我們發現，只要某一猜想成立，上述的唯一性在超出現有解析條件下的維度中依然可以成立。最後，我們證明糾纏傳遞在封閉系統乃一普遍現象。我們證明了在特定的維度下，這些子系統可展現糾纏傳遞，並輔以數值證據支持。我們的結果顯示，本論文討論的三種性質——普遍糾纏、唯一性與糾纏傳遞——在超出現有解析條件下的維度仍有可能成立。

In this thesis, we investigate the behavior of the marginals of generic multipartite pure quantum states. We focus on three questions: when these marginals are almost surely entangled, when they uniquely determine the global state, and when they induce entanglement in other subsystems—a phenomenon known as entanglement transitivity. We find that sufficiently large marginals, if they also consist of many constituents, can almost surely be entangled with respect to every possible bipartition once their size exceeds roughly half of the global system. Generic multipartite pure states are thus robust to losses in entanglement distribution and may be useful for quantum information protocols where the flexible collaboration among subsets of clients is desirable. In certain local dimensions, such marginals uniquely determine the global state, forcing the original generic pure state to be their only possible extension. In contrast, we find that extremal tripartite nonsignaling correlations in the simplest Bell scenario generally lack this uniqueness. To better understand compatibility and uniqueness, we derive the relation between all density matrices that are compatible with a given set of marginals. Based on this, we show that the uniqueness property can hold well in other uncertified local dimensions, provided a conjecture holds. Ultimately, we show that entanglement transitivity is provably generic in closed systems by identifying the local dimensions under which these marginals can exhibit entanglement transitivity, and support these results with numerical evidence which suggests that all three properties—entangled marginals, unique global compatibility, and entanglement transitivity—extend beyond the analytically established dimensional conditions.

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