One-shot and asymptotic classical capacity in general physical theories

Our paper on communication theory beyond quantum theory has recently been published in Physical Review A, a joint work with RIKEN.

One-shot and asymptotic classical capacity in general physical theories

Quantum theory has a very nice mathematical structure. The independent identical distribution acts with very good properties.  One step away from such a "utopia" is the stark wilderness of information theory. Information spectrum theory and one-shot information theory have improved the outlook in such a wilderness. 

Recently, information theory beyond quantum theory is also considered. In 2010, three papers on entropy in general probabilistic theories (GPTs) appeared: 

A. J. Short and S. Wehner, Entropy in general physical theories, New J. Phys. 12, 033023 (2010).
H. Barnum, J. Barrett, L. O. Clark, M. Leifer, R. Spekkens, N. Stepanik, A. Wilce, and R. Wilke, Entropy and information causality in general probabilistic theories, New J. Phys. 12, 033024 (2010).
G. Kimura, K. Nuida, and H. Imai, Distinguishability measures and entropies for general probabilistic theories, Rep. Math. Phys. 66, 175 (2010).

Above these papers suggested operationally valid definitions of entropy in GPTs. They take generally different values but coincide with von Neumann entropy in quantum theory.

Operationally speaking, entropy should be the optimal compression rate of information. Is one of them a universal entropy in GPTs in terms of data compression? According to this paper, no universal entropy in GPTs:

P. Perinotti, A. Tosini, and L. Vaglini, Which entropy for general physical theories?, arXiv:2302.01651 (2023).

In addition to data compression, another major theme of information theory is channel coding, which is about how much information can be sent over channels. It may seem difficult to consider channel coding in GPTs, where even the most basic entropy is complex, but we were able to overcome this problem by starting with considering one-shot information theory in GPTs. In other words, we have discovered that the tools used to explore the wilderness of information theory beyond independent and identical distribution are also useful for exploring information theory beyond quantum theory.