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

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.