Counterfactual quantum measurements

Abstract: Counterfactual reasoning plays a crucial role in exploring hypothetical scenarios, by comparing some consequent under conditions identical except as results from a differing antecedent. David Lewis' well-known analysis evaluates counterfactuals using a hierarchy of desiderata. These were, however, built upon a deterministic classical framework, and whether it could be generalized to indeterministic quantum theory has been an open question. In this Letter, we propose a formalism for quantum counterfactuals in which antecedents are measurement settings. Unlike other approaches, it non-trivially answers questions like: "Given that my photon-detector, observing an atom's fluorescence, clicked at a certain time, what would I have seen using a field-quadrature detector instead?"