Tighter uncertainty and reverse uncertainty relations

Debasis Mondal*, Shrobona Bagchi, Arun Kumar Pati

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


We prove a few state-dependent uncertainty relations for the product as well as the sum of variances of two incompatible observables. These uncertainty relations are shown to be tighter than the Robertson-Schrödinger uncertainty relation and other ones existing in the current literature. Also, we derive a state-dependent upper bound to the sum and the product of variances using the reverse Cauchy-Schwarz inequality and the Dunkl-Williams inequality. Our results suggest that not only can we not prepare quantum states for which two incompatible observables can have sharp values, but also we have both the lower and the upper limits on the variances of quantum mechanical observables at a fundamental level.

Original languageEnglish
Article number052117
JournalPhysical Review A
Issue number5
StatePublished - 18 May 2017
Externally publishedYes


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