2017/01/26 by Boyer, Michel, Brodutch, Aharon, Mor, Tal
#FOS: Physical sciences #Mathematical Physics (math-ph) #Quantum Physics (quant-ph)
paper · doi:10.48550/arxiv.1701.07757
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 neighborhood. We say that such nearby states are ε-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 ε-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 ε, and provide a constructive method for finding ε-discordant states.