Quantum theory of large deviations

Develop a quantum theory of large deviations to provide a quantum counterpart to the classical large-deviation framework for entropy and fluctuation probabilities.

Background

The paper presents classical large-deviation theory, including Sanov’s theorem, as a unifying framework connecting entropy, fluctuations, and statistical mechanics. It then contrasts this established classical theory with quantum entropy and quantum hypothesis testing.

The authors note that existing results commonly called quantum Sanov theorems are generally quantum versions of Stein’s lemma rather than genuine analogues of Sanov’s theorem. They therefore identify the absence of an accepted quantum large-deviation theory as an unresolved problem, while observing that some related quantum hypothesis-testing asymptotics are already available.