gwillen

Oops, I guess I never addressed the "nice pattern" from paragraph 4. In brief: you can represent a probability distribution over N bits with 2**N reals between 0 and 1, in the same way that you can represent a quantum state with N bits using 2**N complex numbers between 0 and 1. In the case of probability, the normalization constraint -- that all the values have to add to 1 -- saves you one of those reals, giving 2**N - 1. Similarly, in quantum mechanics, the normalization constraint saves you one real, and invariance under change of global phase gives you another one, making 2**N - 1 complex numbers.