A nice and interesting property of any pure tensor-product state is that eachsuch state has distillable entangled states at an arbitrarily small distance$\epsilon$ in its neighborhood. We say that such nearby states are$\epsilon$-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 thatproperty mentioned above -- they all have $\epsilon$-entangled states at anysmall distance in their neighborhood. Furthermore, the entanglement they haveis proven to be distillable. We then extend this result to thediscordant/classical cut and show that all classical states (correlated anduncorrelated) have discordant states at distance $\epsilon$, and provide aconstructive method for finding $\epsilon$-discordant states.
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