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Title: Variance control in weak-value measurement pointers

Abstract

The variance of an arbitrary pointer observable is considered for the general case that a complex weak value is measured using a complex valued pointer state. For the typical cases where the pointer observable is either its position or momentum, the associated expressions for the pointer's variance after the measurement contain a term proportional to the product of the weak value's imaginary part with the rate of change of the third central moment of position relative to the initial pointer state just prior to the time of the measurement interaction when position is the observable--or with the initial pointer state's third central moment of momentum when momentum is the observable. These terms provide a means for controlling pointer position and momentum variance and identify control conditions which, when satisfied, can yield variances that are smaller after the measurement than they were before the measurement. Measurement sensitivities which are useful for estimating weak-value measurement accuracies are also briefly discussed.

Authors:
;  [1]
  1. Electromagnetic and Sensor Systems Department, Naval Surface Warfare Center, Dahlgren, Virginia 22448 (United States)
Publication Date:
OSTI Identifier:
22038599
Resource Type:
Journal Article
Journal Name:
Physical Review. A
Additional Journal Information:
Journal Volume: 84; Journal Issue: 1; Other Information: (c) 2011 American Institute of Physics; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 1050-2947
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; 97 MATHEMATICAL METHODS AND COMPUTING; ACCURACY; MEASURING METHODS; QUANTUM MECHANICS

Citation Formats

Parks, A. D., and Gray, J. E.. Variance control in weak-value measurement pointers. United States: N. p., 2011. Web. doi:10.1103/PHYSREVA.84.012116.
Parks, A. D., & Gray, J. E.. Variance control in weak-value measurement pointers. United States. doi:10.1103/PHYSREVA.84.012116.
Parks, A. D., and Gray, J. E.. Fri . "Variance control in weak-value measurement pointers". United States. doi:10.1103/PHYSREVA.84.012116.
@article{osti_22038599,
title = {Variance control in weak-value measurement pointers},
author = {Parks, A. D. and Gray, J. E.},
abstractNote = {The variance of an arbitrary pointer observable is considered for the general case that a complex weak value is measured using a complex valued pointer state. For the typical cases where the pointer observable is either its position or momentum, the associated expressions for the pointer's variance after the measurement contain a term proportional to the product of the weak value's imaginary part with the rate of change of the third central moment of position relative to the initial pointer state just prior to the time of the measurement interaction when position is the observable--or with the initial pointer state's third central moment of momentum when momentum is the observable. These terms provide a means for controlling pointer position and momentum variance and identify control conditions which, when satisfied, can yield variances that are smaller after the measurement than they were before the measurement. Measurement sensitivities which are useful for estimating weak-value measurement accuracies are also briefly discussed.},
doi = {10.1103/PHYSREVA.84.012116},
journal = {Physical Review. A},
issn = {1050-2947},
number = 1,
volume = 84,
place = {United States},
year = {2011},
month = {7}
}