Entropy of an n-system from its correlation with a k-reservoir

Abstract

Let a random pure state vector be chosen in nk‐dimensional Hilbert space, and consider an n‐dimensional subsystem’s density matrix P. P will usually be close to the totally unpolarized mixed state if k is large. Specifically, the rms deviation of a probability from the mean value 1/n is [(1−1/n²)/(kn +1)]^1/2. ’’Random’’ refers to unitarily invariant Haar measure.