We are concerned with the problem of detecting with high probability whether a wave function has collapsed or not, in the following framework: A quantum system with a d-dimensional Hilbert space is initially in state ψ; with probability 0 < p < 1, the state collapses relative to the orthonormal basis b1, …, bd. That is, the final state ψ′ is random, it is ψ with probability 1 − p and bk (up to a phase) with p times Born’s probability . Now an experiment on the system in state ψ′ is desired that provides information about whether or not a collapse has occurred. Elsewhere [C. W. Cowan and R. Tumulka, J. Phys. A: Math. Theor. 47, 195303 (2014)], we identify and discuss the optimal experiment in case that ψ is either known or random with a known probability distribution. Here, we present results about the case that no a priori information about ψ is available, while we regard p and b1, …, bd as known. For certain values of p, we show that the set of ψs for which any experiment is more reliable than blind guessing is at most half the unit sphere; thus, in this regime, any experiment is of questionable use, if any at all. Remarkably, however, there are other values of p and experiments such that the set of ψs for which is more reliable than blind guessing has measure greater than half the sphere, though with a conjectured maximum of 64% of the sphere.
Skip Nav Destination
Research Article| August 26 2015
Detecting wave function collapse without prior knowledge
Charles Wesley Cowan;
Charles Wesley Cowan, Roderich Tumulka; Detecting wave function collapse without prior knowledge. J. Math. Phys. 1 August 2015; 56 (8): 082103. https://doi.org/10.1063/1.4928933
Download citation file: