We introduce a simple sufficient criterion, which allows one to tell whether a subspace of a bipartite or multipartite Hilbert space is entangled. The main ingredient of our criterion is a bound on the minimal entanglement of a subspace in terms of entanglement of vectors spanning that subspace expressed for geometrical measures of entanglement. The criterion is applicable to both completely and genuinely entangled subspaces. We explore its usefulness in several important scenarios. Further, an entanglement criterion for mixed states following directly from the condition is stated. As an auxiliary result we provide a formula for the generalized geometric measure of entanglement of the d-level Dicke states.

我们引入了一个简单的充分标准，它允许人们判断二分或多分希尔伯特空间的子空间是否纠缠。我们标准的主要成分是一个子空间的最小纠缠的界限，就跨越该子空间的向量的纠缠而言，表示为纠缠的几何测量。该标准适用于完全和真正纠缠的子空间。我们探讨了它在几个重要场景中的用处。此外，还说明了直接从该条件得出的混合状态的纠缠标准。作为辅助结果，我们提供了d级 Dicke 态纠缠的广义几何测量公式。