量子纠缠在相對論性時空下的影響

Abstract

我們介紹了量子纠缠在相對論性時空下的影響。第二章介紹了量子纠缠(純態、混和態、量子纠缠的判定、量子纠缠的度量)。第三章介紹了勞侖茲變換在量子力學下的表示 - Wigner旋轉。第四章討論了三個量子纠缠的度量(von Neumann entropy, Concurrence, Negativity)分別在 Minkowski 空間以及彎曲空間下之影響。

We study the entanglement in the relativistic framework. The bipartite quantum state can be classied into pure state or mixed state. One can judge if the pure state is entangled or not by Schmidt decomposition, and the bi-partite entanglement of pure state is quantied by the von Neumann entropy. On the other hand, we adopt the positive partial transpose (PPT) criterion to study the entanglement for the mixed separable states, and quantify it by evaluating the quantities such as the concurrence and negativity. We study the properties of von Neumann entropy, concurrence and negativity under Lorentz transformation. Some examples for the entanglement in the weak and strong gravitational elds are discussed.