What the complex joint probabilities observed in weak measurements can tell us about quantum physics
Abstract
Quantummechanics does not permit joint measurements of noncommuting observables. However, it is possible to measure the weak value of a projection operator, followed by the precise measurement of a different property. The results can be interpreted as complex joint probabilities of the two noncommuting measurement outcomes. Significantly, it is possible to predict the outcome of completely different measurements by combining the joint probabilities of the initial state with complex conditional probabilities relating the new measurement to the possible combinations of measurement outcomes used in the characterization of the quantum state. We can therefore conclude that the complex conditional probabilities observed in weak measurements describe fundamental stateindependent relations between noncommuting properties that represent the most fundamental form of universal laws in quantum physics.
 Authors:

 Graduate School of Advanced Sciences of Matter, Hiroshima University, Kagamiyama 131, Higashi Hiroshima 7398530, Japan and JST, CREST, Sanbancho 5, Chiyodaku, Tokyo 1020075 (Japan)
 Publication Date:
 OSTI Identifier:
 22390698
 Resource Type:
 Journal Article
 Journal Name:
 AIP Conference Proceedings
 Additional Journal Information:
 Journal Volume: 1633; Journal Issue: 1; Conference: 11. International Conference on Quantum Communication, Measurement and Computation, Vienna (Austria), 30 Jul  3 Aug 2012; Other Information: (c) 2014 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 0094243X
 Country of Publication:
 United States
 Language:
 English
 Subject:
 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; COMMUTATION RELATIONS; PROBABILITY; PROJECTION OPERATORS; QUANTUM MECHANICS; QUANTUM STATES
Citation Formats
Hofmann, Holger F. What the complex joint probabilities observed in weak measurements can tell us about quantum physics. United States: N. p., 2014.
Web. doi:10.1063/1.4903083.
Hofmann, Holger F. What the complex joint probabilities observed in weak measurements can tell us about quantum physics. United States. https://doi.org/10.1063/1.4903083
Hofmann, Holger F. Thu .
"What the complex joint probabilities observed in weak measurements can tell us about quantum physics". United States. https://doi.org/10.1063/1.4903083.
@article{osti_22390698,
title = {What the complex joint probabilities observed in weak measurements can tell us about quantum physics},
author = {Hofmann, Holger F.},
abstractNote = {Quantummechanics does not permit joint measurements of noncommuting observables. However, it is possible to measure the weak value of a projection operator, followed by the precise measurement of a different property. The results can be interpreted as complex joint probabilities of the two noncommuting measurement outcomes. Significantly, it is possible to predict the outcome of completely different measurements by combining the joint probabilities of the initial state with complex conditional probabilities relating the new measurement to the possible combinations of measurement outcomes used in the characterization of the quantum state. We can therefore conclude that the complex conditional probabilities observed in weak measurements describe fundamental stateindependent relations between noncommuting properties that represent the most fundamental form of universal laws in quantum physics.},
doi = {10.1063/1.4903083},
url = {https://www.osti.gov/biblio/22390698},
journal = {AIP Conference Proceedings},
issn = {0094243X},
number = 1,
volume = 1633,
place = {United States},
year = {2014},
month = {12}
}