Variance-based uncertainty relations for incompatible observables
Bin Chen, Ning-Ping Cao, Shao-Ming Fei, Gui-Lu Long
TL;DR
This paper develops new variance-based uncertainty relations for multiple incompatible observables, providing stronger bounds than previous inequalities, with detailed examples demonstrating their effectiveness.
Contribution
It introduces novel sum-of-variances uncertainty relations for multiple observables, improving upon existing bounds in most cases.
Findings
New stronger lower bounds for uncertainty relations.
Applicable to arbitrary finite incompatible observables.
Validated with detailed examples.
Abstract
We formulate uncertainty relations for arbitrary finite number of incompatible observables. Based on the sum of variances of the observables, both Heisenberg-type and Schr\"{o}dinger-type uncertainty relations are provided. These new lower bounds are stronger in most of the cases than the ones derived from some existing inequalities. Detailed examples are presented.
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