Abstract
A quantum transition can be seen as a result of interference between various pathways (e.g., Feynman paths), which can be labeled by a variable . An attempt to determine the value of without destroying the coherence between the pathways produces a weak value of . We show to be an average obtained with an amplitude distribution which can, in general, take negative values, which, in accordance with the uncertainty principle, need not contain information about the actual range of which contributes to the transition. It is also demonstrated that the moments of such alternating distributions have a number of unusual properties which may lead to a misinterpretation of the weak-measurement results. We provide a detailed analysis of weak measurements with and without post-selection. Examples include the double-slit diffraction experiment, weak von Neumann and von Neumann–like measurements, traversal time for an elastic collision, phase time, and local angular momentum.
- Received 1 June 2007
DOI:https://doi.org/10.1103/PhysRevA.76.042125
©2007 American Physical Society