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

TL;DR

This paper identifies a large class of separable and classical states that have distillable entangled or discordant states arbitrarily close to them, revealing new insights into quantum state boundaries and correlations.

Contribution

It introduces a vast class of separable states with nearby distillable entanglement and extends the concept to classical states, providing constructive methods to find such states.

Findings

Large class of separable states with nearby distillable entanglement

All classical states have nearby discordant states

Constructive method for finding epsilon-discordant states

Abstract

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 $\epsilon$ 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 that property mentioned above -- they all have $\epsilon$-entangled states at any small distance in their neighborhood. Furthermore, the entanglement they have is proven to be distillable. We then extend this result to the discordant/classical cut and show that all classical states (correlated and uncorrelated) have discordant states at distance $\epsilon$, and provide a constructive method for finding $\epsilon$-discordant states.

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