Postprocessing of quantum instruments

Studying sequential measurements is of the utmost importance to both foundational aspects quantum theory and practical implementations technologies, with these applications being abstractly described by concatenation instruments into a sequence certain length. In general, choice instrument at any given step in can be conditionally chosen based on classical results all preceding instruments. For two we consider conditional second as an effective way post-processing first new one. This similar how measurement positive operator-valued measure (POVM) post-processed another randomization its outcomes using stochastic matrix. this work study relation partial order it induces their equivalence classes. We characterize greatest least element order, give examples post-processings between different types draw connections some induced POVMs.