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 Tuttavia, recentemente è stato dimostrato che la teoria degli strumenti quantistici fornisce una soluzione semplice della combinazione degli effetti QOE e RRE, vedi Ozawa e Khrennikov (2020a)<ref name=":0">Ozawa M., Khrennikov A. Application of theory of quantum instruments to psychology: Combination of question order effect with response replicability effect. Entropy, 22 (1) (2020</ref> per la costruzione di tali strumenti. Tali strumenti sono di tipo non proiettivo. Pertanto, l'essenza della QOE non è nella struttura degli osservabili, ma nella struttura della trasformazione dello stato generata dal feedback delle misurazioni. QOE non riguarda la misurazione congiunta e l'incompatibilità (non commutatività) di osservabili, ma la misurazione sequenziale di osservabili e l'aggiornamento sequenziale dello stato (mentale). Gli strumenti quantistici utilizzati in Ozawa e Khrennikov (2020a)<ref name=":0" /> per combinare QOE e RRE corrispondono alla misurazione delle osservabili rappresentate dagli operatori di commutazione <math>\widehat{A},\widehat{B} </math>. Inoltre, è possibile dimostrare che (sotto restrizione matematica naturale) QOE e RRE possono essere modellati congiuntamente solo con l'ausilio di strumenti quantistici per la commutazione di osservabili.
-===6.3. “QOE+RRE”: described by quantum instruments of non-projective type===
-In paper (Khrennikov et al., 2014), it was shown that by using the von Neumann calculus it is ''impossible to combine RRE with QOE.'' To generate QOE, Hermitian operators  <math>\widehat{A},\widehat{B} </math> should be noncommutative, but the latter destroys<math>A-B-A </math> response replicability of  <math>A </math>. This was a rather unexpected result. It made even impression that, although the basic cognitive effects can be quantum-likely modeled separately, their combinations cannot be described by the quantum formalism.
-However, recently it was shown that theory of quantum instruments provides a simple solution of the combination of QOE and RRE effects, see Ozawa and Khrennikov (2020a) for construction of such instruments. These instruments are of non-projective type. Thus, the essence of QOE is not in the structure of observables, but in the structure of the state transformation generated by measurements’ feedback. QOE is not about the joint measurement and incompatibility (noncommutativity) of observables, but about sequential measurement of observables and sequential (mental-)state update. Quantum instruments which are used in Ozawa and Khrennikov (2020a) to combine QOE and RRE correspond to measurement of observables represented by commuting operators <math>\widehat{A},\widehat{B} </math>. Moreover, it is possible to prove that (under natural mathematical restriction) QOE and RRE can be jointly modeled only with the aid of quantum instruments for commuting observables.