Does conditional entropy squeezing indicate normalized entropic uncertainty relation steering?

TL;DR

This paper introduces a new method using average conditional entropy squeezing to assess NEUR-steering in two-qubit systems, showing strong correlation with existing measures and sensitivity to quantum processes.

Contribution

It presents a novel approach linking conditional entropy squeezing with NEUR-steering, including derived expressions and comparative analysis for different quantum states.

Findings

Complete similarity in maximally entangled states

Comparable behavior with minor deviations in partially entangled states

Proportional effect of quantum processes like acceleration and noise

Abstract

A novel approach is introduced to assess one-way Normalized Entropic Uncertainty Relations (NEUR)-steering in a two-qubit system by utilizing an average of conditional entropy squeezing. The mathematical expressions of conditional entropy squeezing and NEUR-steering are derived and presented. To gain a better understanding of the relationship between the two measures, a comparative analysis is conducted on a set of two-qubit states. Our results reveal that the two measures exhibit complete similarity when applied to a maximally entangled state, while they display comparable behavior with minor deviations for partially entangled states. Additionally, it is observed that the two measures are proportionally affected by some quantum processes such as acceleration, noisy channels, and swapping. As a result, the average of conditional entropy squeezing proves to be an effective indicator of NEUR-steering.