On sequential measurements with indefinite causal order

Abstract

Two projective measurements sequentially performed on a quantum system is studied in the case that the order of the measurements is completely indefinite. The interference of the different orders provides the Kirkwood-Dirac distribution of a quantum system to be measured and thus the weak value of an observable can be obtained without weak measurement. In an interferometric setting, the Kirkwood-Dirac distribution can be constructed from conditional visibility and phase shift.