Abstract
Quantum correlations which violate a Bell inequality are presumed to power better-than-classical protocols for solving communication complexity problems (CCPs). How general is this statement? We show that violations of correlation-type Bell inequalities allow advantages in CCPs, when communication protocols are tailored to emulate the Bell no-signaling constraint (by not communicating measurement settings). Abandonment of this restriction on classical models allows us to disprove the main result of, inter alia, \cite{BZ02}; we show that quantum correlations obtained from these communication strategies assisted by a small quantum violation of the CGLMP Bell inequalities do not imply advantages in any CCP in the input/output scenario considered in the reference. More generally, we show that there exists quantum correlations, with nontrivial local marginal probabilities, which violate the I3322 Bell inequality, but do not enable a quantum advantange in any CCP, regardless of the communication strategy employed in the quantum protocol, for a scenario with a fixed number of inputs and outputs
Highlights
Entanglement in itself cannot be used for information transfer
Whereas we do not provide a decisive answer to whether Bell nonlocality always implies advantages in Communication complexity problems (CCPs), we show that there exists a natural input/output scenario in which Bell nonlocality does not enable a quantum advantage in any CCP
A substantial number of examples of quantum advantages in CCPs being powered by Bell inequality violations can be understood as different instances of a single map from Bell inequalities to CCPs
Summary
Entanglement in itself cannot be used for information transfer. when combined with classical communication, it becomes a paradigmatic resource for quantum information transfer. Immediately the following entanglement-assisted strategy becomes relevant: Alice and Bob use their inputs (x, y) as settings in a quantum test of the CHSH inequality where a, b ∈ [2] are their respective local outcomes. Since shared entanglement enables Alice and Bob to violate the CHSH inequality, this quantum strategy leads to a score of up to. [22], that every violation of the CGLMP inequality combined with the above mentioned communication strategies implies an advantage in some CCP for a fixed number of inputs and outputs The classical simulation of entanglement-assisted CCPs. We consider a situation with fixed number of inputs and outputs and show that there exists a quantum nonlocal probability distribution that does not enable better-than-classical communication complexity, regardless of the communication strategy and the choice of score. Our results are in opposition to the common belief that Bell nonlocality always is useful for better-than-classical communication complexity
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