Abstract

We generalize the concept of unbiasedness from bases to measurements. We show that mutually unbiased (MU) measurements, which are not necessarily von Neumann measurements, exist in all finite-dimensional Hilbert spaces. We study the geometrical relation between these measurements and symmetric informationally complete measurements. In particular we find that these two kinds of measurements are related to each other as points and lines in finite affine plane geometries. This relation provides a natural way to define discrete phase-space functions based on MU measurements and symmetric informationally complete measurements.

Date

June 12, 2014

Authors

Amir Kalev

Journal

Journal of Physics A: Mathematical and Theoretical

Volume

47

Issue

26

Pages

265301

Publisher

IOP Publishing