Extrapolated States, Void States, and a Huge Novel Class of Distillable Entangled States

摘要

A nice and interesting property of any pure tensor-product state is that each such state has distillable entangled states at an arbitrarily small distance ε in its neighbourhood. We say that such nearby states are ∈-entangled, and we call the tensor product state in that case, a "boundary separable state", as there is entanglement at any distance from this "boundary". Here we find a huge class of separable states that also share that property mentioned above - they all have ∈-entangled states at any small distance in their neighbourhood. Furthermore, the entanglement they have is proven to be distillable.