English

All measurements in a probabilistic theory are compatible if and only if the state space is a simplex

Quantum Physics 2016-10-26 v1

Abstract

We study the compatibility of measurements on finite-dimensional compact convex state space in the framework of general probabilistic theory. Our main emphasis is on formulation of necessary and sufficient conditions for two-outcome measurements to be compatible and we use these conditions to show that there exist incompatible measurements whenever the state space is not a simplex. We also formulate the linear programming problem for the compatibility of two-outcome measurements.

Keywords

Cite

@article{arxiv.1608.05614,
  title  = {All measurements in a probabilistic theory are compatible if and only if the state space is a simplex},
  author = {Martin Plávala},
  journal= {arXiv preprint arXiv:1608.05614},
  year   = {2016}
}