A Tsirelson bound and mixed states.

[jk22]

Could it be possible that using a mixed stated $\rho=\sum_{i=1}^4|\langle e_i|\Psi\rangle|^2|e_i\rangle\langle e_i|$

Where $\Psi$ is the singlet state and the $e_i$ form an orthonormal basis (like an intermediary state),That one could violate Tsirelson's bound if the parameters describing the basis could depend on the angle of measurements ? (The latter would imply that this intermediary state basis would be at the recollecting of both side's datas)

 

[DarMM]

Violating Tsirelson's bound permits unobserved levels of information transfer. Specifically if you had Alice and Bob each with one particle from an entangled pair it would allow Bob to learn the value of $m$ bits from a dataset of Alice's by her transmitting $n < m$ bits.

Also it would imply that observables that are pairwise joint measurable are not totally joint measurable, e.g. $\{A,B\}$, $\{B,C\}$ and $\{A,C\}$ are all joint measurable but $\{A,B,C\}$ is not. This contradicts QM and isn't observed in practice.