A classical interpretation of the Scrooge distribution

Abstract

The Scrooge distribution is a probability distribution over the set of pure states of a quantum system. Specifically, it is the distribution that, upon measurement, gives up the least information about the identity of the pure state, compared with all other distributions having the same density matrix. The Scrooge distribution has normally been regarded as a purely quantum mechanical concept, with no natural classical interpretation. In this paper we offer a classical interpretation of the Scrooge distribution viewed as a probability distribution over the probability simplex. We begin by considering a real-amplitude version of the Scrooge distribution, for which we find that there is a non-trivial but natural classical interpretation. The transition to the complex-amplitude case requires a step that is not particularly natural but that may shed light on the relation between quantum mechanics and classical probability theory.

17 pages; for a special issue of Entropy: Quantum Communication--Celebrating the Silver Jubilee of Teleportation

References in corpus (5)

• Introduction to the book "Quantum Theory: Informational Foundations and Foils"
• Typicality of pure states randomly sampled according to the Gaussian adjusted projected measure
• Average coherence and its typicality for random mixed quantum states
• Smoothness of Wave Functions in Thermal Equilibrium
• On the properties of information gathering in quantum and classical measurements

Cited by in corpus (1)

• Quantum Communication -- Celebrating the Silver Jubilee of Teleportation