「貝爾（Bell）非局域性」是量子力學最重要的性質之一，利用這個性質，其中一個在近幾年來吸引著許多人注意的重要應用為「與設備無關的量子資訊過程」。背後的一個主要因素是，在進行實驗時的測量設備可以被視為黑箱，意即我們不需要對這些設備做太多物理上的假設，這樣的工具可以使得實驗學家在利用不可能百分之百完美的測量設備時，仍然可以相信最後的實驗結果。

量子力學有個另外的重要現象－「量子操縱性」。簡單來說，量子操縱性讓我們僅經由量測自己的系統，可以為遙遠的另一端準備不同基底的量子態，而這個「如鬼魅般的超距作用」的現象在古典力學是不可能發生的。

已經有研究指出，所有具有非局域性的量子態，必定也有操縱性，即：量子操縱性為系統之間擁有量子關聯性的必要條件。本論文的工作之一即是量化此性質，意即在觀測到某個程度的非局域性量子態的情況之下，需要多少程度的操縱性在系統之間。

上述的量子關聯性是發生在兩個或以上的系統之間的量子現象。然而，如果我們考慮在不同時間點的同一個系統，也可以擁有區別於古典的時間量子關聯性。其中一個重要的時間量子關聯性的概念是由萊格特（A. J. Leggett）和加爾格（A. Garg）提出的，這種關聯性時常又被稱做為「時間上的貝爾非局域性」。受到這個工作的啟發，本論文的另一個工作是探索量子操縱性是否也存在著時間上的版本－「時間量子操縱性」，並且研究其相對應的物理意涵以及應用。

Bell nonlocality is one of the most intriguing phenomena in quantum mechanics. An important application by using nonlocality of quantum states as a resource is device-independent (DI) quantum information processing, which has attracted a lot of attentions recently. A main reason is that one can treat the devices as black boxes, and few assumptions on the operations of the devices are made. Such a black-box scheme makes an experiment feasible even when the devices are imperfect.

Quantum steering is a phenomenon in quantum theory that allows one party to instantaneously and remotely prepare the set of quantum states for the other spatially separated party, merely by the former party’s choice of measurement settings. This can not happen in a locally hidden state model, from which the measurement outcomes of one party and the quantum states of the other party are predetermined by some hidden variables. The resource of such “spooky action at a distance” provides inspirations and many applications in the foundation of quantum mechanics and in quantum information sciences.

Indeed, there exists relations between steering and nonlocality. More precisely, all nonlocal quantum states are also steerable, but not vice versa. One of the main works of this thesis is to quantify such a property, i.e., obtaining a lower bound of steerability when given a nonlocal correlations.

Quantum phenomena can also occur in a single system at different moments of time. A famous example is the existence of dynamics which does not fulfill the joint assumption of non-invasive measurability and macroscopic realism. This can be witnessed by the violation of a Leggett-Garg inequality, which is also treated as a temporal analogue of a Bell inequality. Motivated by this, we would like to develop a temporal analogue of quantum steering and refer to this new concept as temporal steering, which is the other main work of this thesis, and several applications are also given.

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