Stronger uncertainty relations for all incompatible observables

The Heisenberg-Robertson uncertainty relation expresses a limitation in the possible preparations of the system by giving a lower bound to the product of the variances of two observables in terms of their commutator. Notably, it does not capture the concept of incompatible observables because it can...

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Bibliographic Details
Published in:Physical review letters 2014-12, Vol.113 (26), p.260401-260401, Article 260401
Main Authors: Maccone, Lorenzo, Pati, Arun K
Format: Article
Language:English
Subjects:
Commutators
Lower bounds
Uncertainty
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Summary:The Heisenberg-Robertson uncertainty relation expresses a limitation in the possible preparations of the system by giving a lower bound to the product of the variances of two observables in terms of their commutator. Notably, it does not capture the concept of incompatible observables because it can be trivial; i.e., the lower bound can be null even for two noncompatible observables. Here we give two stronger uncertainty relations, relating to the sum of variances, whose lower bound is guaranteed to be nontrivial whenever the two observables are incompatible on the state of the system.
ISSN:0031-9007
1079-7114
DOI:10.1103/PhysRevLett.113.260401