Mutually unbiased bases and bound entanglement

In this contribution we relate two different key concepts: mutually unbiased bases (MUBs) and entanglement. We provide a general toolbox for analyzing and comparing entanglement of quantum states for different dimensions and numbers of particles. In particular we focus on bound entanglement, i.e. highly mixed states which cannot be distilled by local operations and classical communications. For a certain class of states—for which the state-space forms a 'magic' simplex—we analyze the set of bound entangled states detected by the MUB criterion for different dimensions d and number of particles n. We find that the geometry is similar for different d and n, consequently the MUB criterion opens possibilities to investigate the typicality of positivity under partial transposition (PPT)-bound and multipartite bound entanglement more deeply and provides a simple experimentally feasible tool to detect bound entanglement. (paper)