| [typo note its 2^N quantum amplitudes] A clear description but potentially very misleading and one that will certainly screw up your intuition about what to expect from quantum computers. As pointed out below, a classical probability distribution of N bits is a 2^N dimensional vector of real numbers. There are many very good reasons to think of the quantum state as "more like" this classical vector than the physical state of the "N classical bits" themselves. Here is one: - If I send you the physical systems which encode N classical bits then sure enough, I can communicate to you only N classical bits of information despite it taking exponentially many real parameters to specify the distribution/state I prepared them in. - If I send you the physical systems which encode N quantum bits then sure enough, I can communicate to you only N classical bits of information despite it taking exponentially many real parameters to specify the distribution/state I prepared them in. There are many other reasons to think of quantum states as not "inherently real" and more like the classical probability distribution. A key one is that both "instantaneously collapse" when you get information about the outcome of an observation. The issue of course is that while we know the "real states of the world are" of a conventional computer, nobody agrees on what (if any) they are for quantum systems (though many constraints on such purported real states are known, I write about some of them in _Q is for Quantum_) |
(check out https://en.wikipedia.org/wiki/Superdense_coding)