论文标题
两个子系统的任何定义的纠缠
Entanglement for any definition of two subsystems
论文作者
论文摘要
量子状态的纠缠概念通常是针对固定两部分的。实际上，全球基础变化总是可以将纠缠状态映射到可分离状态。但是，在考虑一组状态时，情况有所不同。在这项工作中，我们定义了量子状态的“绝对纠结”的概念：对于全球基础的任何可能选择，集合中的至少一个状态是纠缠的。因此，对于所有两部分，即子系统的任何可能的定义，该集合都具有纠缠。我们提供了这个现象的最低示例，其中包含$ \ Mathbb {C}^4 = \ Mathbb {C}^2 \ otimes \ Mathbb {C}^2 $的四个状态。此外，我们提出了一种绝对集纠缠的定量措施。为了降低该数量，我们开发了一种基于多项式优化的方法，以对单位的单位进行凸优化，这是独立的。
The notion of entanglement of quantum states is usually defined with respect to a fixed bipartition. Indeed, a global basis change can always map an entangled state to a separable one. The situation is however different when considering a set of states. In this work we define the notion of an "absolutely entangled set" of quantum states: for any possible choice of global basis, at least one of the states in the set is entangled. Hence, for all bipartitions, i.e. any possible definition of the subsystems, the set features entanglement. We present a minimum example of this phenomenon, with a set of four states in $\mathbb{C}^4 = \mathbb{C}^2 \otimes \mathbb{C}^2$. Moreover, we propose a quantitative measure for absolute set entanglement. To lower-bound this quantity, we develop a method based on polynomial optimization to perform convex optimization over unitaries, which is of independent interest.
