经典张量与量子纠缠I：纯态
Classical Tensors and Quantum Entanglement I: Pure States
摘要：
与量子系统相关联的希尔伯特空间的几何描述考虑厄米张量来描述矢量的标量内积，现在由矢量场描述。这个张量的实部表示平坦的黎曼度量张量，而虚部表示辛二形式。经典流形在与希尔伯特空间相关的复射影空间中的浸入允许通过浸入映射拉回与先前张量场相关的张量场。这使得可用，对这些选定的流形的状态，方法通常黎曼和辛几何。在这里，我们考虑这些拉回张量场时，浸入子流形包含可分离态或纠缠态。几何张量编码这些状态的一些属性。这些结果与文献中已有的标准不无关系。我们明确地处理其中的一些关系。
英文摘要：
The geometrical description of a Hilbert space asociated with a quantum system considers a Hermitian tensor to describe the scalar inner product of vectors which are now described by vector fields. The real part of this tensor represents a flat Riemannian metric tensor while the imaginary part represents a symplectic two-form. The immersion of classical manifolds in the complex projective space associated with the Hilbert space allows to pull-back tensor fields related to previous ones, via the immersion map. This makes available, on these selected manifolds of states, methods of usual Riemannian and symplectic geometry. Here we consider these pulled-back tensor fields when the immersed submanifold contains separable states or entangled states. Geometrical tensors are shown to encode some properties of these states. These results are not unrelated with criteria already available in the literature. We explicitly deal with some of these relations.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
