Maximum Quantum Entropy for classical density functions

Maximum Quantum Entropy (MQE), recently introduced by Richard Silver and also known as Quantum Statistical Inference (QSI), is a method of estimating smooth, non-quantum-mechanical (''classical'') densities, given information about those densities. It is formally analogous to Maximum Entropy (ME), the difference being that the Shannon entropy is replaced by the quantum entropy. We present a concise description of MQE from a mathematical perspective, not relying on physical analogy. We introduce density matrices and the quantum entropy, compare MQE with ME, discuss the nature of constraints in MQE and show how these constraints influence the density estimate. We conclude with a discussion of the status of MQE as a maximum entropy method.