Rényi Entropy, Signed Probabilities, and the Qubit

Abstract

The states of the qubit, the basic unit of quantum information, are $2\times 2$ 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.

13 pages, 1 figure

References in corpus (3)

• Quantum Mechanics as Quantum Information (and only a little more)
• Implausible Consequences of Superstrong Nonlocality
• Discrete phase space and minimum-uncertainty states

Cited by in corpus (3)

• Qubit from the classical collision entropy
• Efficient measure of information backflow with a quasistochastic process
• Ideal stochastic process modeling with post-quantum quasiprobabilistic theories