Entropy of an <i>n</i>-system from its correlation with a <i>k</i>-reservoir 论文

摘要

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.