Fig. 2: Irreversibility of temporal coarse-graining.
From: Extracting quantum dynamical resources: consumption of non-Markovianity for noise reduction
(Left) Temporal coarse-graining transitions between levels of temporal accessibility/resolution to the same underlying process: from fine resolution to coarse resolution. (Right) This transition is inherently irreversible, as described in Obs. 1. Fewer transformations are possible after performing temporal coarse-graining than before. Explicitly, given a process \({{{{\bf{T}}}}}_{\hat{n}}\), one can immediately coarse-grain to \({{{{\bf{T}}}}}_{\hat{m}}\) (m ≤ n), or first apply a superprocess \({{{{\bf{Z}}}}}_{\hat{n}\hat{n}}\) to obtain \({{{{\bf{T}}}}}_{\hat{n}}^{{\prime} }\), which is subsequently coarse-grained to \({{{{\bf{T}}}}}_{\hat{m}}^{{\prime} }\). From this perspective, noise reduction occurs when the application of \({{{{\bf{Z}}}}}_{\hat{n}\hat{n}}\) resulted in \({{{{\bf{T}}}}}_{\hat{m}}^{{\prime} }\) having greater mutual information between its intputs and outputs compared to \({{{{\bf{T}}}}}_{\hat{m}}\).
