Optimal Guessing Strategies in a Quantum Card Game

Three different quantum cards which are non-orthogonal quantum bits are sent to two different players, Alice and Bob, randomly. Alice receives one of the three cards, and Bob receives the remaining two cards. We find that Bob could know better than Alice does on guessing Alice's card, no matter what Bob chooses to measure his two cards collectively or separately. We also find that Bob's best strategy for guessing Alice's card is to measure his two cards collectively.