Local-Stochastic Correlated Quantum Noise

Use the finite channel-location schedule from Finite ordered channel-location schedules and its location set $L$. Let $(\mathrm{\Omega },w)$ be a finite probability space and $F:\mathrm{\Omega }\to \mathcal{P}(L)$ a random fault set. Its law is $\eta$-local-stochastic as in Local-Stochastic Fault-Set Law. For each pattern $F\subseteq L$ and each $\mathrm{\ell }\in F$, specify a CPTP replacement map supported on the same declared support $S_{\mathrm{\ell }}$ as the ideal channel at $\mathrm{\ell }$. The replacement at one location may depend on the full pattern $F$. For each outcome, the conditional noisy denotation is the chronological schedule obtained by using those replacements at faulty locations and the ideal channels elsewhere. It is a composition of per-location channels; the model does not add a joint operation across distinct locations.

This is a separate noise model from the independent local replacement model. Its probability hypothesis is the bound on every specified subset of fault locations; it does not assert independence. Correlation is allowed in the fault-set law and in the pattern-dependent choice of local fault maps, while each map remains attached to its own location.