Fig. 5: Aharonov and Vaidman’s protocol overlaid with a counterfactuality-violating history.

The modified protocol proposed by Aharonov and Vaidman in ref. ¹¹, of which we show one cycle, cannot be said to be counterfactual from a consistent histories viewpoint. This can be seen from the series of projections, or history, highlighted in blue. The thin vertical lines represent non-polarising beamsplitters, thick vertical lines represent mirrors, and the blue path shows an example of a history where, when Bob doesn't block, the photon travels to Bob and back to Alice’s relevant detector with nonzero probability. See text for mathematical details.