Causality and Tsirelson's bounds

We study the properties of no-signaling correlations that cannot be reproduced by local measurements on entangled quantum states. We say that such correlations violate Tsirelson bounds. We show that if these correlations are obtained by some reversible unitary quantum evolution U, then U cannot be written in the product form U₀U₁. This implies that U can be used for signaling and for entanglement generation. This result is completely general and in fact can be viewed as a characterization of Tsirelson bounds. We then show how this result can be used as a tool to study Tsirelson bounds and we illustrate this by rederiving the Tsirelson bound of 22 for the Clauser-Horn-Shimony-Holt inequality, and by deriving a new Tsirelson bound for qutrits.