Counterfactual control and quantum contextuality in multi-mode interferometers

As shown in previous work, quantum contextuality can be represented by interference effects in a three-path interferometer. A Hardy-like paradox is obtained when the absence of photons in two internal paths seems to contradict the presence of photons in a specific input port. Here, we consider the effects of counterfactual control on this scenario by analyzing the changes to the paths through the interferometer when the seemingly impossible input path is blocked. The effects on photons that never interact with the absorber in the blocked path reveals a characteristic signature of quantum contextuality that may help to explain why quantum interference is incompatible with measurement independent realities.