Entropic uncertainty relations for multiple measurements

Abstract

We present the entropic uncertainty relations for multiple measurement settings in quantum mechanics. Those uncertainty relations are obtained for both cases with and without the presence of quantum memory. They take concise forms which can be proven in a unified method and easy to calculate. Our results recover the well known entropic uncertainty relations for two observables, which show the uncertainties about the outcomes of two incompatible measurements. Those uncertainty relations are applicable in both foundations of quantum theory and the security of many quantum cryptographic protocols.

11 pages (including the appendix), 2 figures

References in corpus (4)

• Quantum information can be negative
• Experimental non-classicality of an indivisible quantum system
• Competitions between quantum correlations in the quantum-memory-assisted entropic uncertainty relation
• State-independent experimental tests of quantum contextuality in a three dimensional system

Cited by in corpus (6)

• Uncertainty Relations for Quantum Coherence
• Uncertainties of genuinely incompatible triple measurements based on statistical distance
• Uncertainty Relation Based on Skew Information with Quantum Memory
• Entropic Uncertainty Relations via Direct-Sum Majorization Relation for Generalized Measurements
• Enhanced Information Exclusion Relations
• Using Stein's estimator to correct the bound on the entropic uncertainty principle for more than two measurements