Discrete Wigner Functions from Informationally Complete Quantum Measurements

Abstract

Wigner functions provide a way to do quantum physics using quasiprobabilities, that is, "probability" distributions that can go negative. Informationally complete POVMs, a subject that has been developed more recently than Wigner's time, are less familiar but provide wholly probabilistic representations of quantum theory. We study how these two classes of structure relate and the art of interconverting between them. Pushing Wigner functions to their limits, in a suitably quantified sense, reveals a new way in which the Symmetric Informationally Complete quantum measurements (SICs) are significant.