  We describe a new technique for obtaining Tsirelson bounds, or upper bounds
on the quantum value of a Bell inequality. Since quantum correlations do not
allow signaling, we obtain a Tsirelson bound by maximizing over all
no-signaling probability distributions. This maximization can be cast as a
linear program. In a setting where three parties, A, B, and C, share an
entangled quantum state of arbitrary dimension, we: (i) bound the trade-off
between AB's and AC's violation of the CHSH inequality, and (ii) demonstrate
that forcing B and C to be classically correlated prevents A and B from
violating certain Bell inequalities, relevant for interactive proof systems and
cryptography.
