Stronger error disturbance relations for incompatible quantum measurements
Harish-Chandra Research Institute - Chhatnag Road, Jhunsi, Allahabad 211 019, India
Received: 28 December 2015
Accepted: 8 March 2016
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 a particular class of joint measurements under consideration. We also prove a modified form of Ozawa's error-disturbance relation. The latter relation provides a tighter bound compared to the Ozawa and the Branciard inequalities for a small number of states.
PACS: 03.65.Ta – Foundations of quantum mechanics; measurement theory / 03.65.Ca – Formalism / 03.65.Aa – Quantum systems with finite Hilbert space
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