Tighter Uncertainty and Reverse Uncertainty Relations

Abstract

We prove a few novel state-dependent uncertainty relations for product as well the sum of variances of two incompatible observables. These uncertainty relations are shown to be tighter than the Roberson-Schrödinger uncertainty relation and other ones existing in the current literature. Also, we derive 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 we cannot prepare quantum states for which two incompatible observables can have sharp values, but also we have both, lower and upper limits on the variances of quantum mechanical observables at a fundamental level.

4+ε, 4 figures, comments are welcome

References in corpus (8)

• Heisenberg's Uncertainty Principle
• Stronger uncertainty relations for the sum of variances
• Experimental investigation of the stronger uncertainty relations for all incompatible observables
• Sum Uncertainty Relation in Quantum Theory
• Weighted Uncertainty Relations
• Characterization of quantum angular-momentum fluctuations via principal components
• Products of weak values: uncertainty relations, complementarity and incompatibility
• Implications and applications of the variance-based uncertainty equalities

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