Entanglement and designs
Matthew A. Graydon, D. M. Appleby · Journal of Physics A Mathematical and Theoretical · 2016
We describe a connection between entanglement and designs. It involves the conical two-designs introduced in a previous paper. These are a generalization of projective two-designs which includes full sets of arbitrary rank mutually unbiased measurements ( mum s) and arbitrary rank symmetric informationally complete measurements ( sim s), as well as the more familiar mub s and sic s. We show that a povm is a conical two-design if and only if there exists what we call a regular entanglement monotone whose restriction to the pure states is a function of the norm of the probability vector. In that case the concurrence is such a monotone. We also generalize and develop previous work on designs and entanglement detection.