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Phys. Rev. Lett. 60, 1103–1106 (1988)

Generalized entropic uncertainty relations

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Hans Maassen
Institute for Theoretical Physics, University of Nijmegen, 6525 ED Nijmegen, The Netherlands

J. B. M. Uffink
Institute for Theoretical Physics, University of Amsterdam, 1018 XE Amsterdam, The Netherlands

Received 18 November 1987; published in the issue dated 21 March 1988

A new class of uncertainty relations is derived for pairs of observables in a finite-dimensional Hilbert space which do not have any common eigenvector. This class contains an ‘‘entropic’’ uncertainty relation which improves a previous result of Deutsch and confirms a recent conjecture by Kraus. Some comments are made on the extension of these relations to the case where the Hilbert space is infinite dimensional.

© 1988 The American Physical Society

URL:
http://link.aps.org/doi/10.1103/PhysRevLett.60.1103
DOI:
10.1103/PhysRevLett.60.1103
PACS:
03.65.Bz