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The quantum three-box paradox considers a ball prepared in a superposition ofbeing in one of three Boxes. Bob makes measurements by opening either Box 1 orBox 2. After performing some unitary operations (shuffling), Alice can inferwith certainty that the ball was detected by Bob, regardless of which box heopened, if she detects the ball after opening Box 3. The paradox is that theball would have been found with certainty in either box, if that box had beenopened. Resolutions of the paradox include that Bob's measurement cannot bemade non-invasively, or else that realism cannot be assumed at the quantumlevel. Here, we strengthen the case for the former argument, by constructingmacroscopic versions of the paradox. Macroscopic realism implies that the ballis in one of the boxes, prior to Bob or Alice opening any boxes. We demonstrateconsistency of the paradox with macroscopic realism, if carefully defined (asweak macroscopic realism, wMR) to apply to the system at the times prior toAlice or Bob opening any Boxes, but after the unitary operations associatedwith preparation or shuffling. By solving for the dynamics of the unitaryoperations, and comparing with mixed states, we demonstrate agreement betweenthe predictions of wMR and quantum mechanics: The paradox only manifests ifAlice's shuffling combines both local operations (on Box 3) and nonlocaloperations, on the other Boxes. Following previous work, the macroscopicparadox is shown to correspond to a violation of a Leggett-Garg inequality,which implies non-invasive measurability, if wMR holds.

A macroscopic quantum three-box paradox: finding consistency with weak macroscopic realism