Monotones in Resource Theories for Dynamical Decoupling

TL;DR

This paper refines the resource quantifiers in a dynamical resource theory framework for noise reduction, ensuring they are monotonic and consistent with the theory, and reinterprets previous numerical results accordingly.

Contribution

It introduces modified relative entropy-based resource quantifiers that are proven to be monotonic within the framework, improving the theoretical foundation of dynamical decoupling analysis.

Findings

New monotonic resource quantifiers confirmed for the theory

Numerical results reinterpreted with the new monotones

Noise reduction correlates with decreases in non-Markovianity

Abstract

In arXiv:2110.02613, we presented a generalised dynamical resource theory framework that enabled noise reduction techniques including dynamical decoupling (DD) to be studied. While this fundamental contribution remains correct, it has been found that the main resource quantifiers we employed to study these resource theories -- based on the relative entropies between Choi states of multitime processes -- are not monotonic under the allowed transformations. In this letter we detail modified relative entropy-based resource quantifiers, prove that they are indeed monotonic in our resource theories. We re-interpret our numerical results in terms of these new relative entropy monotones, arriving at the same empirical conclusions: DD can be understood as temporal resource distillation, and improvements to noise reduction via our multitimescale optimal dynamical decoupling (MODD) method coincide with a decrease in the corresponding non-Markovianity monotone.