论文标题
纠缠与量子状态内的可分离性之间的内部边界
Internal Boundary between Entanglement and Separability Within a Quantum State
论文作者
论文摘要
量子状态是量子力学中的关键数学对象，纠缠位于量子信息处理和计算的新生场的核心。但是，没有一个通用，必要和足够的操作分离性条件来确定任意量子状态是纠缠还是可分离的。在本文中，我们表明量子状态是否纠缠不清，是由量子状态内的阈值确定的。我们首先介绍了\ emph {finer}的概念，并根据可分离状态在高级证人的作用中的属性，\ emph {optimal}可分离状态。然后，我们表明，任何两部分量子状态都可以分解为其最佳纠缠状态及其最佳分离状态的凸混合物。此外，我们表明，任意量子状态是纠缠还是可分离的，以及积极的部分换位（PPT），是由其最佳纠缠状态符合至关重要阈值的最佳纠缠状态到其最佳可分离状态的稳健性。此外，对于任意量子状态，我们提供了操作算法，以获得其最佳的纠缠状态，最佳的可分离状态，最佳的可分离近似（BSA）分解和最佳的PPT近似分解，这是一个开放的问题，即如何计算高差异系统中的BSA。
Quantum states are the key mathematical objects in quantum mechanics, and entanglement lies at the heart of the nascent fields of quantum information processing and computation. However, there has not been a general, necessary and sufficient, and operational separability condition to determine whether an arbitrary quantum state is entangled or separable. In this paper, we show that whether a quantum state is entangled or not is determined by a threshold within the quantum state. We first introduce the concept of \emph{finer} and \emph{optimal} separable states based on the properties of separable states in the role of higher-level witnesses. Then we show that any bipartite quantum state can be decomposed into a convex mixture of its optimal entangled state and its optimal separable state. Furthermore, we show that whether an arbitrary quantum state is entangled or separable, as well as positive partial transposition (PPT) or not, is determined by the robustness of its optimal entangled state to its optimal separable state with reference to a crucial threshold. Moreover, for an arbitrary quantum state, we provide operational algorithms to obtain its optimal entangled state, its optimal separable state, its best separable approximation (BSA) decomposition, and its best PPT approximation decomposition while it was an open question that how to calculate the BSA in high-dimension systems.
