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  in its neighborhood. We say that such nearby states are -entangled, and we call the tensor product state in that case, a “boundary separa- ble state,” as there is entanglement at any distance from this “boundary.” Here we find a huge class of separable states that also share the property mentioned above—they all have - entangled states at any small distance in their neighborhood. Furthermore, the entanglement they have is proved to be dis-
tillable. We then extend this result to the discordant/classical cut and show that all classical states (correlated and uncor- related) have discordant states at distance , and provide a constructive method for finding -discordant states.

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