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Communication complexity problems (CCPs) are tasks in which separated partiesattempt to compute a function whose inputs are distributed among the parties.Their communication is limited so that not all inputs can be sent. We show thatbroad classes of Bell inequalities can be mapped to CCPs and that a quantumviolation of a Bell inequality is a necessary and sufficient condition for anenhancement of the related CCP beyond its classical limitation. However, onecan implement CCPs by transmitting a quantum system, encoding no moreinformation than is allowed in the CCP, and extract information by performingmeasurements. We show that for a large class of Bell inequalities, theimprovement of the CCP associated to a quantum violation of a Bell inequalitycan be no greater than the improvement obtained from quantumprepare-transmit-measure strategies.

physical review. a/physical review, a

Higher dimensional communication complexity problems: classical  protocols vs quantum ones based on Bell's Theorem or prepare-transmit-measure  schemes