Stronger Error Disturbance Relations for Incompatible Quantum Measurements

Abstract

We formulate a new error-disturbance relation, which is free from explicit dependence upon variances in observables. This error-disturbance relation shows improvement over the one provided by the Branciard inequality and the Ozawa inequality for some initial states and for particular class of joint measurements under consideration. We also prove a modified form of Ozawa's error-disturbance relation. The later relation provides a tighter bound compared to the Ozawa and the Branciard inequalities for a small number of states.

5+pages, 3 figures

References in corpus (7)

• Heisenberg's Uncertainty Principle
• Stronger uncertainty relations for the sum of variances
• Quantum root-mean-square error and measurement uncertainty relations
• Measurement uncertainty relations
• Entropic information-disturbance tradeoff
• Direct tests of measurement uncertainty relations: what it takes
• Connection between Measurement Disturbance Relation and Multipartite Quantum Correlation

Cited by in corpus (5)

• Tighter Uncertainty and Reverse Uncertainty Relations
• State-independent preparation uncertainty relations
• Entropic uncertainty relations for successive measurements of canonically conjugate observables
• Uncertainty Relation for Non-Hermitian Systems
• Quantum uncertainty relation based on the mean deviation