Optimized entropic uncertainty relations for multiple measurements

TL;DR

This paper improves and optimizes entropic uncertainty bounds for multiple quantum measurements, providing tighter relations that enhance understanding and security in quantum information processing.

Contribution

It introduces a new constructed bound (SCB) and an optimized version (OSCB) that are tighter than previous bounds for multiple measurements.

Findings

SCB is tighter than Liu et al.'s bound for mutually unbiased bases

The optimized bound (OSCB) considers mutual information and Holevo quantity

Proposed bounds extend the behavior from two to multiple measurements

Abstract

Recently, an entropic uncertainty relation for multiple measurements has been proposed by Liu et al. in [Phys. Rev. A 91, 042133 (2015)]. However, the lower bound of the relation is not always tight with respect to different measurements. Herein, we improve the lower bound of the entropic uncertainty relation for multiple measurements, termed as simply constructed bound (SCB). We verify that the SCB is tighter than Liu et al.'s result for arbitrary mutually unbiased basis measurements, which might play a fundamental and crucial role in practical quantum information processing. Moreover, we optimize the SCB by considering mutual information and the Holevo quantity, and propose an optimized SCB (OSCB). Notably, the proposed bounds are extrapolations of the behavior of two measurements to a larger collection of measurements. It is believed that our findings would shed light on entropy-based uncertainty relations in the multiple measurement scenario and will be beneficial for security analysis in quantum key distributions.