Nonlocality transitivity exists for quantum states, shown by explicit constructions using Bell-inequality tensoring and occurring in Haar-random three-qutrit states.
Monogamy of Bell correlations and Tsirelson's bound
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abstract
We consider three parties, A, B, and C, each performing one of two local measurements on a shared quantum state of arbitrary dimension. We characterize the trade-off between the nonlocality of the Bell correlations observed by AB and of those observed by AC. This generalizes Tsirelson's bound on the quantum value of the CHSH inequality, the latter being recovered when C is completely uncorrelated with AB. We also discuss the trade-off between Bell violations and local expectation values of observables that anticommute with the ones used in the Bell test.
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quant-ph 2representative citing papers
A single N-qubit state can violate all binom(N,k) Bell inequalities for its (N-k)-partite subsystems at once, with the effect extending across multiple subsystem sizes via hyper-polygamy.
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Nonlocality of Quantum States can be Transitive
Nonlocality transitivity exists for quantum states, shown by explicit constructions using Bell-inequality tensoring and occurring in Haar-random three-qutrit states.