  Counter-intuitive to classical notions, quantum conditional entropy can be
negative, playing a pivotal role in information-processing tasks. This article
delves deeply into quantum channels, emphasizing negative conditional entropy
breaking channels (NCEB) and introducing negative conditional entropy
annihilating channels (NCEA). We characterize these channels from both
topological and information-theoretic perspectives, examining their properties
when combined serially and NCEB in parallel. Our exploration extends to
complimentary channels associated with NCEB, leading to the introduction of
information-leaking channels. Utilizing the parameters of the standard
depolarizing channel, we provide tangible examples and further
characterization. We demonstrate the relationship of NCEB and NCEA with newly
introduced channels like coherent information breaking (CIB) and mutual
information breaking (MIB), along with standard channels like zero capacity
channels. Preservation of quantum resources is an integral constituent of
quantum information theory. Recognizing this, we lay prescriptions to detect
channels that do not break the negativity of conditional entropy, ensuring the
conservation of this quantum resource.
