Adam Brandenburger, Pierfrancesco La Mura, and Stuart Zoble's "Rényi Entropy, Signed Probabilities, and the Qubit"

October 12, 2022

The states of the qubit, the basic unit of quantum information, are 2×2 positive semi-definite Hermitian matrices with trace 1. We contribute to the program to axiomatize quantum mechanics by characterizing these states in terms of an entropic uncertainty principle formulated on an eight-point phase space. We do this by employing Rényi entropy (a generalization of Shannon entropy) suitably defined for the signed phase-space probability distributions that arise in representing quantum states.

Adam Brandenburger is the J.P. Valles Professor of Business Economics and Strategy at NYU Stern.
Read the full paper here.