# Unitary induced channels and Tsirelson's problem

## TL;DR

This paper explores the relationship between quantum commuting and tensor models through the lens of unitary induced channels, providing new characterizations and linking them to Tsirelson's conjecture without infinite-dimensional measurements.

## Contribution

It offers an equivalent formulation of Tsirelson's conjecture using generalized unitary induced channels and demonstrates a difference between quantum commuting and tensor models.

## Key findings

- Equivalent characterization of unitary induced channels in tensor and commuting paradigms
- Formulation of Tsirelson's conjecture without infinite-dimensional measurements
- Identification of differences between quantum commuting and tensor models for these channels

## Abstract

Motivated by a recent progress concerning quantum commuting and quantum tensor models of composed systems we investigate a notion of (generalized) unitary induced quantum channel. Using properties of Brown algebras we provide an equivalent characterization of discussed families in both tensor and commuting paradigms. In particular, we provide an equivalent formulation of Tsirelson's conjecture (Connes' embedding problem) in terms of considered paradigms based on protocols which do not require measurements performed on infinite-dimensional subsystems. As a result we show that there is a difference between quantum commuting and quantum tensor models for generalized unitary induced channels.