论文标题
量子力学中纯状态边缘问题的完整层次结构
A complete hierarchy for the pure state marginal problem in quantum mechanics
论文作者
论文摘要
澄清整个部分之间的关系对于许多科学中的许多问题至关重要。在量子力学中，这个问题在量子边缘问题中表现出来，该问题询问某些给定边缘的量子是否存在全球纯量子状态。这个问题在许多情况下出现，从量子化学到纠缠理论和量子误差校正代码等等。在本文中，我们证明了边际问题与可分离性问题的对应关系。基于此，我们描述了一系列半决赛程序，这些程序可以决定一些给定的边缘是否与某些纯净的全球量子状态兼容。作为一种应用，我们证明，给定维度绝对最大纠缠的多粒子的存在等效于显式给定的两方量子状态的可分离性。最后，我们表明，具有给定参数的量子代码的存在也可以解释为边缘问题，因此，我们的完整层次结构也可以使用。
Clarifying the relation between the whole and its parts is crucial for many problems in science. In quantum mechanics, this question manifests itself in the quantum marginal problem, which asks whether there is a global pure quantum state for some given marginals. This problem arises in many contexts, ranging from quantum chemistry to entanglement theory and quantum error correcting codes. In this paper, we prove a correspondence of the marginal problem to the separability problem. Based on this, we describe a sequence of semidefinite programs which can decide whether some given marginals are compatible with some pure global quantum state. As an application, we prove that the existence of multiparticle absolutely maximally entangled states for a given dimension is equivalent to the separability of an explicitly given two-party quantum state. Finally, we show that the existence of quantum codes with given parameters can also be interpreted as a marginal problem, hence, our complete hierarchy can also be used.
