A task in which separated players receive local questions and return local answers, with a joint winning condition and no communication after questions are received. A strategy may use pre-shared randomness, or pre-shared quantum entanglement when quantum resources are allowed. An average winning probability requires a specified input distribution; winning with certainty on every promised input is a separate worst-case requirement. The GHZ game gives a finite example with a perfect quantum strategy and no perfect classical strategy.
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