Reverse Data-Processing Theorems and Computational Second Laws
Abstract
Drawing on an analogy with the second law of thermodynamics for adiabatically isolated systems, Cover argued that data-processing inequalities may be seen as second laws for "computationally isolated systems," namely, systems evolving without an external memory. Here we develop Cover's idea in two ways: on the one hand, we clarify its meaning and formulate it in a general framework able to describe both classical and quantum systems. On the other hand, we prove that also the reverse holds: the validity of data-processing inequalities is not only necessary, but also sufficient to conclude that a system is computationally isolated. This constitutes an information-theoretic analogue of Lieb's and Yngvason's entropy principle. We finally speculate about the possibility of employing Maxwell's demon to show that adiabaticity and memorylessness are in fact connected in a deeper way than what the formal analogy proposed here prima facie seems to suggest.
Keywords
Cite
@article{arxiv.1607.08335,
title = {Reverse Data-Processing Theorems and Computational Second Laws},
author = {Francesco Buscemi},
journal= {arXiv preprint arXiv:1607.08335},
year = {2019}
}
Comments
ver2: discussions clarified, typos corrected, references added, and yet, still 24 pages and 2 figures; ver1: 24 pages, 2 figures. Contribution to the proceedings of the Nagoya Winter Workshop on Quantum Information, Measurement, and Foundations (March 2015)