TL;DR
This paper provides a simple proof that quantum entropy increases when two ensembles are combined, supporting the foundation of quantum information theory.
Contribution
It offers an elementary proof of quantum entropy's incremental property within the broader framework of matrix entropies.
Findings
Quantum entropy increases upon ensemble union.
Supports the proof of strong subadditivity of quantum entropy.
Introduces an elementary proof within matrix entropy framework.
Abstract
Incremental information, as measured by the quantum entropy, is increasing when two ensembles are united. This result was proved by Lieb and Ruskai, and it is the foundation for the proof of strong subadditivity of quantum entropy. We present a truly elementary proof of this fact in the context of the broader family of matrix entropies introduced by Chen and Tropp.
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