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Correlation coefficients and Robertson-Schroedinger uncertainty relations

Fleming, Gordon N. (2007) Correlation coefficients and Robertson-Schroedinger uncertainty relations. [Preprint]

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    Abstract

    Calling the quantity; 2ΔAΔB/|<[A, B]>|, with non-zero denominator, the uncertainty product ratio or UPR for the pair of observables, (A, B), it is shown that any non-zero correlation coefficient between two observables raises, above unity, the lower bound of the UPR for each member of an infinite collection of pairs of incompatible observables. Conversely, any UPR is subject to lower bounds above unity determined by each of an infinite collection of correlation coefficients. This result generalizes the well known Schroedinger strengthening of the Robertson uncertainty relations (with the former expressed in terms of the correlation coefficient rather than the anticommutator) where the UPR and the correlation coefficient both involve the same pair of observables. Two, independent, derivations of the result are presented to clarify its’ origins and some examples of its’ use are examined.


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    Item Type: Preprint
    Additional Information: 15 pages, 1 figure
    Keywords: uncertainty relations, correlation coefficients, Robertson-Schroedinger, master inequality
    Subjects: Specific Sciences > Physics > Quantum Mechanics
    Depositing User: Gordon N. Fleming
    Date Deposited: 25 Mar 2007
    Last Modified: 07 Oct 2010 11:15
    Item ID: 3262
    URI: http://philsci-archive.pitt.edu/id/eprint/3262

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