The quantum three-box paradox is a prototypical example of some bizarre predictions for intermediate measurements made on pre- and postselected systems. Although in principle those effects can be explained by measurement disturbance, it is not clear what mechanisms are required to fully account for the observed correlations. In this paper, this paradox is scrutinized from the causal point of view. We consider an array of potential causal structures behind the experiment, eliminating those without enough explanatory power. A distinction is made between the propagation in the system of just the measurement outcome and the information about the full measurement context. We also discuss the consequences of the realist position in which preexisting values are revealed by measurements. Interestingly, the answers depend crucially on whether the original version of the paradox is considered or its extension where the third box is allowed for inspection too. This illustrates the richness of the paradox which is better appreciated from the causal perspective.
We introduce a new paradox, which we call Counterfactual Local Friendliness (CLF): a Wigner's-friend-type logical collision in which every decisive inference is obtained by interaction-free flags whose disturbance on the probed object is bounded by a tunable parameter
ε. Under (Q) universal unitarity for outside observers, (S) single-outcome facts, (C) cross-agent consistency, and (IF-
ε)
ε-counterfactuality of the friends' internal modules, quantum theory predicts a nonzero post-selected event that forces mutually incompatible certainties about a single upstream variable -- without appealing to absorptive or projective in-lab measurements. We also derive an
ε-IF three-box noncontextual bound: any single-world, noncontextual model satisfying exclusivity and epsilon-stability must obey
P(A)+P(B)≤1+Kε, while quantum theory yields
P(A)=P(B)=1, violating the bound for arbitrarily small
ε. Together these results isolate what is paradoxical about counterfactual phenomena: not energy exchange with the probed system, but the incompatibility of agent-level facts in single-world narratives.
The quantum three-box paradox considers a ball prepared in a superposition of being in any one of three boxes. Bob makes measurements by opening either box 1 or box 2. After performing some unitary operations (shuffling), Alice can infer with certainty that the ball was detected by Bob, regardless of which box he opened, if she detects the ball after opening box 3. The paradox is that the ball would have been found with certainty by Bob in either box if that box had been opened. Resolutions of the paradox include that Bob’s measurement cannot be made non-invasively or else that realism cannot be assumed at the quantum level. Here, we strengthen the case for the former argument by constructing macroscopic versions of the paradox. Macroscopic realism implies that the ball is in one of the boxes prior to Bob or Alice opening any boxes. We demonstrate the consistency of the paradox with macroscopic realism, if carefully defined (as weak macroscopic realism, wMR) to apply to the system at the times prior to Alice or Bob opening any boxes but after the unitary operations associated with preparation or shuffling. By solving for the dynamics of the unitary operations and comparing with mixed states, we demonstrate agreement between the predictions of wMR and quantum mechanics: the paradox only manifests if Alice’s shuffling combines both local operations (on box 3) and nonlocal operations, on the other boxes. Following previous work, the macroscopic paradox is shown to correspond to a violation of a Leggett–Garg inequality, which implies failure of non-invasive measurability if wMR holds.