Consider a quantum system prepared in state psi, a unit vector in a d-dimensional Hilbert space. Let b_1,...,b_d be an orthonormal basis and suppose that, with some probability 0View original: http://arxiv.org/abs/1307.0810
|^2. The question we investigate is: How well can any quantum experiment on the system determine afterwards whether a collapse has occurred? The answer depends on how much is known about the initial vector psi. We prove a number of different results addressing several variants of the question. In each case, no experiment can provide more than rather limited probabilistic information. In the case of psi unknown, but drawn from a uniform distribution over the unit sphere in Hilbert space, no experiment performs better than a blind guess without measurement; that is, no experiment provides any useful information. The following results concern the case that no_a_priori_ information about psi is available, not even a probability distribution from which psi was sampled: For certain values of p, we show that the set of psis for which any experiment E is more reliable than blind guessing is at most half the unit sphere; thus, any experiment is of questionable use, if any at all. Remarkably, however, there are other values of p and experiments E such that the set of psis for which E is more reliable than blind guessing has measure greater than half the sphere, though with a conjectured maximum of 64% of the sphere.