Unitary induced channels and Tsirelson’s problem

Motivated by recent progress concerning quantum commuting and quantum tensor product models of composed systems, we investigate a notion of (generalized) unitary induced quantum channels. Using properties of Brown algebras, we provide a characterization of these families of channels in both the tensor and commuting frameworks. In particular, we introduce a reformulation of Tsirelson's conjecture (equivalently, Connes' embedding problem) in terms of the considered paradigms, based on protocols that do not require measurements on infinite-dimensional subsystems. As a result, we show that there is a separation between quantum commuting and quantum tensor product models for (generalized) unitary induced channels. Specifically, this difference can be observed by parties with direct access only to finite-dimensional subsystems.