Optimal Uncertainty Relations for Extremely Coarse-grained Measurements

Abstract

We derive two quantum uncertainty relations for position and momentum coarse-grained measurements. Building on previous results, we first improve the lower bound for uncertainty relations using the Renyi entropy, particularly in the case of coarse-grained measurements. We then sharpen a Heisenberg-like uncertainty relation derived previously in [Europhys. Lett. 97, 38003, (2012)] that uses variances and reduces to the usual one in the case of infinite precision measurements. Our sharpened uncertainty relation is meaningful for any amount of coarse graining. That is, there is always a non-trivial uncertainty relation for coarse-grained measurement of the non-commuting observables, even in the limit of extremely large coarse graining.

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• Tightening the tripartite quantum memory assisted entropic uncertainty relation
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• Certainty relations, mutual entanglement and non-displacable manifolds
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• Entropic uncertainty relations for mutually unbiased periodic coarse-grained observables resemble their discrete counterparts
• Coarse-grained dynamics in quantum many-body systems using the maximum entropy principle
• Transition to the classical regime in quantum mechanics on a lattice and implications of discontinuous space
• Classifying Measurement Incompatibility under Classical Pre- and Post-Processing Operations