Detecting wave function collapse without prior knowledge

作者：Cowan Charles Wesley^*; Tumulka Roderich

来源：Journal of Mathematical Physics, 2015, 56(8): 082103.

DOI：10.1063/1.4928933

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 psi; with probability 0 < p < 1, the state collapses relative to the orthonormal basis b(1),...,b(d). That is, the final state psi' is random, it is psi with probability 1 - p and b(k) (up to a phase) with p times Born's probability vertical bar < b(k)vertical bar psi >vertical bar(2). Now an experiment on the system in state psi' 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 psi is either known or random with a known probability distribution. Here, we present results about the case that no a priori information about psi is available, while we regard p and b(1),...,b(d) as known. For certain values of p, we show that the set of psi s for which any experiment epsilon 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 epsilon such that the set of psi s for which epsilon is more reliable than blind guessing has measure greater than half the sphere, though with a conjectured maximum of 64% of the sphere.

• 出版日期2015-8
• 单位rutgers