Weak values, 'negative probability', and the uncertainty principle
- School of Mathematics and Physics, Queen's University of Belfast, Belfast, BT7 1NN (United Kingdom)
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 f. An attempt to determine the value of f without destroying the coherence between the pathways produces a weak value of f. We show f 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 f 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.
- OSTI ID:
- 21020667
- Journal Information:
- Physical Review. A, Vol. 76, Issue 4; Other Information: DOI: 10.1103/PhysRevA.76.042125; (c) 2007 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA); ISSN 1050-2947
- Country of Publication:
- United States
- Language:
- English
Similar Records
Path summation and von Neumann-like quantum measurements
Uncertainty relations for positive-operator-valued measures