Classical Information Transmission via Majorization Relations in Quantum Channels

In this work, we investigate a communication framework based on majorization relations between quantum states. Instead of encoding information directly into quantum states, classical symbols are associated with relational structures such as comparability and incomparability under majorization. We focus on qutrit systems and analyze how these relations behave under the action of quantum channels, in particular depolarizing and dephasing noise models. Through explicit examples, we show how classical information can be transmitted by exploiting the ordering structure of state ensembles and how quantum noise affects the preservation of these relations. We further discuss a simple protocol in which decoding is performed by identifying majorization relations between received states, highlighting the role of spectral properties rather than state distinguishability. Our results indicate that, although this relational encoding provides an alternative perspective for information transmission in quantum systems, its performance is strongly dependent on the channel dynamics.