Free versus Bound Entanglement: Machine learning tackling a NP-hard problem

• URL: http://arxiv.org/abs/2106.03977v1
• Date: Mon, 7 Jun 2021 21:38:39 GMT
• Title: Free versus Bound Entanglement: Machine learning tackling a NP-hard problem
• Authors: Beatrix C. Hiesmayr
• Abstract summary: Entanglement detection in high dimensional systems is a NP-hard problem since it is lacking an efficient way. We find a family of magically symmetric states of bipartite qutrits for which we find $82%$ to be free entangled, $2%$ to be certainly separable and as much as $10%$ to be bound entangled.
• Score: 0.06091702876917279
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Entanglement detection in high dimensional systems is a NP-hard problem since it is lacking an efficient way. Given a bipartite quantum state of interest free entanglement can be detected efficiently by the PPT-criterion (Peres-Horodecki criterion), in contrast to detecting bound entanglement, i.e. a curious form of entanglement that can also not be distilled into maximally (free) entangled states. Only a few bound entangled states have been found, typically by constructing dedicated entanglement witnesses, so naturally the question arises how large is the volume of those states. We define a large family of magically symmetric states of bipartite qutrits for which we find $82\%$ to be free entangled, $2\%$ to be certainly separable and as much as $10\%$ to be bound entangled, which shows that this kind of entanglement is not rare. Via various machine learning algorithms we can confirm that the remaining $6\%$ of states are more likely to belonging to the set of separable states than bound entangled states. Most important we find via dimension reduction algorithms that there is a strong $2$-dimensional (linear) sub-structure in the set of bound entangled states. This revealed structure opens a novel path to find and characterize bound entanglement towards solving the long-standing problem of what the existence of bound entanglement is implying.

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