Uncertainties of genuinely incompatible triple measurements based on statistical distance

Abstract

We investigate the measurement uncertainties of a triple of positive operator-valued measures (POVMs) based on statistical distance, and formulate state-independent tight uncertainty inequalities satisfied by the three measurements in terms of triple-wise joint measurability. Particularly, uncertainty inequalities for three unbiased qubit measurements are presented with analytical lower bounds which relates to the necessary and sufficient condition of the triple-wise joint measurability of the given triple. We show that the measurement uncertainties for a triple measurement are essentially different from the ones obtained by pair wise measurement uncertainties by comparing the lower bounds of different measurement uncertainties.

arXiv comment6 pages, 2 figures

References in corpus (29)

• The Uncertainty Principle in the Presence of Quantum Memory
• Heisenberg's Uncertainty Principle
• Universally valid reformulation of the Heisenberg uncertainty principle on noise and disturbance in measurement
• Entropic uncertainty relations - A survey
• Stronger uncertainty relations for the sum of variances
• Uncertainty Relations for Noise and Disturbance in Generalized Quantum Measurements
• Proof of Heisenberg's error-disturbance relation
• Quantum root-mean-square error and measurement uncertainty relations
• Improved entropic uncertainty relations and information exclusion relations
• Universal Uncertainty Relations
• Majorization entropic uncertainty relations
• Noise and disturbance in quantum measurements: an information-theoretic approach
• Entropic uncertainty relations for multiple measurements
• Heisenberg uncertainty for qubit measurements
• Uncertainty Relations for Angular Momentum
• Experimental test of Heisenberg's measurement uncertainty relation based on statistical distances
• Sum Uncertainty Relation in Quantum Theory
• Heisenberg Uncertainty Relation for Three Canonical Observables
• Experimental test of entropic noise-disturbance uncertainty relations for spin-1/2 measurements
• Experimental Demonstration of Uncertainty Relations for the Triple Components of Angular Momentum
• Strong entropic uncertainty relations for multiple measurements
• Tight entropic uncertainty relations for systems with dimension three to five
• Multi-observable Uncertainty Relations in Product Form of Variances
• Measurement uncertainty relations for discrete observables: Relative entropy formulation
• Improved Uncertainty Relation in the Presence of Quantum Memory
• Geometry of Uncertainty Relations for Linear Combinations of Position and Momentum
• Universality in Uncertainty Relations for a Quantum Particle
• Optimal Universal Uncertainty Relations
• Uncertainty relations and information loss for spin-1/2 measurements

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• Optimizing incompatible triple quantum measurements
• A Note on Hierarchy of Quantum Measurement Incompatibilities
• Identifying the $3$-qubit $W$ state with quantum uncertainty relation
• Observing tight triple uncertainty relations in two-qubit systems
• Entropic measurement uncertainty relations for all the infinite components of a spin vector