Testing incompatibility of quantum devices with few states

Teiko Heinosaari, Takayuki Miyadera, Ryo Takakura

Published 2021-05-18, updated 2021-05-27Version 2

When observations must come from incompatible devices and cannot be produced by compatible devices? This question motivates two integer valued quantifications of incompatibility, called incompatibility dimension and compatibility dimension. The first one quantifies how many states are minimally needed to detect incompatibility if the test states are chosen carefully, whereas the second one quantifies how many states one may have to use if they are randomly chosen. With concrete examples we show that these quantities have unexpected behaviour with respect to noise.