量子混態的量子糾纏純化研究

Abstract

雖然最近幾年有許多值得一提的突破性的進展，以高的純度傳輸一個量子 態到遙遠的地方依然是ㄧ個挑戰。為了完成這目標，量子傳輸(Quantum Teleportation)是一個很強大的方法。它能傳輸一個未知態到另一個地點。但是被 傳輸的態的純度跟事先被傳輸的量子貝爾糾纏對的純度有關係。透過量子糾纏對 才能執行量子傳輸。除此之外，量子糾纏在量子資訊和量子通訊中都扮演著非 常重要的角色，例如量子金鑰傳輸(QKD)、量子超密傳輸(Quantum Superdense Coding)。因為量子態比起古典的訊號是更脆弱，所以在量子通道中傳輸時量子態 容易受到環境的干擾而使得原本的量子純態變成混態。這篇論文會介紹能夠除去 位元錯誤和相位錯誤的協定即使它們同時發生。此外，藉著線性光學元件和單光 子偵測器我們提出一個可以純化貝爾對角態的機率式協定。此外，跟其他的機率 式純化協定不同的是，我們提出的協定能純化大的位元錯誤率和相位錯誤率的糾 纏混態。更重要的是我們提出一個可以百分之百純化貝爾對角態的協定，而且使 用者能知道所想要的糾纏對何時與在何處產生。

Transmitting a quantum state with high fidelity to a distant place is still a challenge even though there are some ramarkable breakthroughs recently. Quantum teleportation, which distributes an unknown state to a distant place, is one of powerful ways to achieve this goal. But the fidelity of the teleported state depends on the fidelity of the distributed entangled Bell pairs, through which Alice and Bob can implement the quantum teleportation protocol. Besides, quantum entanglement plays a vital role in quantum information and quantum communication, such as in quantum key distribution (QKD) and quantum superdense coding. A quantum state is more fragile than a classical signal. When transmitting a quantum state through a quantum channel, a quantum state tends to be disturbed by noise from the environment so that a pure state becomes a mixed state. We introduce some protocols through which one can enhance the fidelity of mixed entangled pairs even when simultaneous bit-flip error and phase-flip error occur. Specicially, we propose a probablistic protocol purifying mixed Bell diagonal states to a higher-fidelity entangled state by passive linear optical components and single-photon detectors. Besides, unique from other probablistic protocols, our proposed protocol has a characteristic to purify mixed entangled states with either large bit-flip error probability or large phase-flip error probability. Moreover, we propose a deterministic protocol using spatial entanglement, which allows users to know where and when the desired output of polarization entangled photon pair comes out.