Does conditional entropy squeezing indicate normalized entropic uncertainty relation steering?

A novel approach is introduced to assess one-way normalized Entropic Uncertainty Relation (EUR)-steering in a two-qubit system by utilizing an average of conditional entropy squeezing. The mathematical expressions of conditional entropy squeezing and normalized EUR-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. Interestingly, 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. Notably, we observe that the two measures are interrelated, meaning that any change in one measure corresponds directly to a similar change in the other. However, if a variance arises in their behavior, it is usually minor and attributable to the external environment, such as acceleration, noisy channels, and swapping. This characteristic highlights the effectiveness of average conditional entropy squeezing as an indicator of normalized EUR-steering.