Journal of Physics A Mathematical and Theoretical

Mutually unbiased probability-operator measurements

Amir Kalev

Published Jun 12, 2014• 20 citations

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.

DOI: 10.1088/1751-8113/47/26/265301

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