Can One Detect Whether a Wave Function Has Collapsed?

Abstract

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 $0<p<1$, $\psi$ ``collapses,'' i.e., gets replaced by $b_k$ (possibly times a phase factor) with Born's probability $|⟨b_k|\psi ⟩{|}^2$. 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 provide 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 case $\psi$ is drawn randomly with 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.

19 pages LaTeX, 8 figures. The first version of this paper has been (revised and) split into two papers, the first of which is v2 of this post, and the second part is posted as arXiv:1312.7321

References in corpus (2)

• On the Common Structure of Bohmian Mechanics and the Ghirardi-Rimini-Weber Theory
• The Quantum Formalism and the GRW Formalism

Cited by in corpus (2)

• Epistemology of Wave Function Collapse in Quantum Physics
• Detecting Wave Function Collapse Without Prior Knowledge