Entanglement of $\pi$-LME states and the SAT problem
Abstract
In this paper we investigate the entanglement properties of the class of -locally maximally entanglable (-LME) states, which are also known as the "real equally weighted states" or the "hypergraph states". The -LME states comprise well-studied classes of quantum states (e.g. graph states) and exhibit a large degree of symmetry. Motivated by the structure of LME states, we show that the capacity to (efficiently) determine if a -LME state is entangled would imply an efficient solution to the boolean satisfiability (SAT) problem. More concretely, we show that this particular problem of entanglement detection, phrased as a decision problem, is -complete. The restricted setting we consider yields a technically uninvolved proof, and illustrates that entanglement detection, even when quantum states under consideration are highly restricted, still remains difficult.
Keywords
Cite
@article{arxiv.1405.7429,
title = {Entanglement of $\pi$-LME states and the SAT problem},
author = {Adi Makmal and Markus Tiersch and Vedran Dunjko and Shengjun Wu},
journal= {arXiv preprint arXiv:1405.7429},
year = {2014}
}