A classical interpretation of the Scrooge distribution

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

Entanglement and Composite Bosons

We build upon work by C. K. Law [Phys. Rev. A 71, 034306 (2005)] to show in general that the entanglement between two fermions largely determines the extent to which the pair behaves like an elementary boson. Specifically, we derive upper and lower bounds on a quantity that governs the bosonic character of a pair of fermions when N such pairs approximately share the same wavefunction. Our bounds depend on the purity of the single-particle density matrix, an indicator of entanglement, and demonstrate that if the entanglement is sufficiently strong, the quantity in question approaches its ideal bosonic value.Comment: 10 page