Lower bound of quantum uncertainty from extractable classical information

TL;DR

This paper establishes a new form of entropic uncertainty relation where the lower bound is determined by extractable classical information, highlighting the role of classical correlations in quantum uncertainty reduction.

Contribution

It introduces a novel uncertainty relation expression linking the bound to extractable classical information, applicable to various quantum states including separable states with discord.

Findings

Lower bound matches fine-graining results for certain states.

Classical correlations can reduce uncertainty even without quantum correlations.

The relation applies to both pure and mixed entangled states.

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.