Lower bound of quantum uncertainty from extractable classical information

Abstract

The sum of entropic uncertainties for the measurement of two non-commuting observables is not always reduced by the amount of entanglement (quantum memory) between two parties, and in certain cases may be impacted by quantum correlations beyond entanglement (discord). An optimal lower bound of entropic uncertainty in the presence of any correlations may be determined by fine-graining. Here we express the uncertainty relation in a new form where the maximum possible reduction of uncertainty is shown to be given by the extractable classical information. We show that the lower bound of uncertainty matches with that using fine-graining for several examples of two-qubit pure and mixed entangled states, and also separable states with non-vanishing discord. Using our uncertainty relation we further show that even in the absence of any quantum correlations between the two parties, the sum of uncertainties may be reduced with the help of classical correlations.

12 pages, 2 figures, accepted for publication in Quantum Information Processing

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• Controlling the entropic uncertainty lower bound in two-qubit systems under the decoherence
• Entropic uncertainty relation in Garfinkle-Horowitz-Strominger dilation black hole
• Holevo bound of entropic uncertainty relation under Unruh channel in the context of open quantum systems
• Entropic uncertainty and quantum non-classicality of Unruh-Dewitt detectors in relativity
• Tripartite measurement uncertainty in Schwarzschild space-time
• Tripartite quantum-memory-assisted entropic uncertainty relations for multiple measurements
• Quantumness and entropic uncertainty for a pair of static Unruh-DeWitt detectors