Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Annals of the New York Academy of Sciences

Minimal Uncertainty and Maximal Information for Quantum Position and Momentum

PEKKA J. LAHTI

Published Dec 1, 1986• 1 citation
Publisher
DOI
10.1111/j.1749-6632.1986.tb12469.x

Related papers

States of minimal uncertainty and maximal information for position and momentum observables in quantum theory

PEKKA J. LAHTI

Reports on Mathematical Physics•Jun 1, 1986•9 citations

Minimal uncertainty and maximal information for quantum position and momentum

Paul Busch, PEKKA J. LAHTI

In view of the recently proposed entropic uncertainty relations several characterisations of 'maximal information' and 'minimal uncertainty' are compared and applied to position and momentum. It is argued that a sufficiently refined entropic uncertainty relation might require the general concept of POV observables as used in stochastic quantum mechanics.

Journal of Physics A Mathematical and General•Mar 11, 1987•9 citations

Uncertainty and quantum mechanics

Tim Freegarde

Cambridge University Press eBooks•Nov 8, 2012•0 citations

Quantum Uncertainty

Pieter Kok

Undergraduate lecture notes in physics•Jan 1, 2023•0 citations

Quantum observables: Compatibility versus commutativity and maximal information

Paul Busch, Thomas P. Schonbek, Franklin E. Schroeck

Two different approaches to a characterization of the degree of (in)compatibility of quantum observables are investigated. First, recent examples of the (partial) commutativity of spectral measures of incompatible observables are proved to be generic. The analysis is extended to the case of compatible or incompatible unsharp, or stochastic observables, leading to a general criterion for commutativity of position and momentum effects. Further, a recently proposed information theoretic quantification of the (in)compatibility of noncommuting observables is generalized, and the relation between ‘‘maximal information,’’ ‘‘minimal uncertainty,’’ partial commutativity, and strict correlation is further clarified. Both approaches are illustrated in a number of examples.

Journal of Mathematical Physics•Dec 1, 1987•23 citations

Information Exclusion Principle for Complementary Observables

Michael J. W. Hall

The sum of the information gains corresponding to measurements of position and momentum is bounded by $\mathrm{log}2\ensuremath{\Delta}X\ensuremath{\Delta}P/\ensuremath{\hbar}$ for a quantum ensemble with position and momentum uncertainties $\ensuremath{\Delta}X$ and $\ensuremath{\Delta}P$. The bound implies the Heisenberg uncertainty principle and that the gain of position information can be maximized only at the expense of momentum information, and vice versa. This exclusion principle for the information contents of complementary observables is extended to finite Hilbert spaces, and to the quadrature, number, and phase observables of bosonic fields degraded by Gaussian noise.

Physical Review Letters•Apr 24, 1995•88 citations
Two different approaches to a characterization of the degree of (in)compatibility of quantum observables are investigated. First, recent examples of the (partial) commutativity of spectral measures of incompatible observables are proved to be generic. The analysis is extended to the case of compatible or incompatible unsharp, or stochastic observables, leading to a general criterion for commutativity of position and momentum effects. Further, a recently proposed information theoretic quantification of the (in)compatibility of noncommuting observables is generalized, and the relation between ‘‘maximal information,’’ ‘‘minimal uncertainty,’’ partial commutativity, and strict correlation is further clarified. Both approaches are illustrated in a number of examples.
The sum of the information gains corresponding to measurements of position and momentum is bounded by $\mathrm{log}2\ensuremath{\Delta}X\ensuremath{\Delta}P/\ensuremath{\hbar}$ for a quantum ensemble with position and momentum uncertainties $\ensuremath{\Delta}X$ and $\ensuremath{\Delta}P$. The bound implies the Heisenberg uncertainty principle and that the gain of position information can be maximized only at the expense of momentum information, and vice versa. This exclusion principle for the information contents of complementary observables is extended to finite Hilbert spaces, and to the quadrature, number, and phase observables of bosonic fields degraded by Gaussian noise.