O papel da discriminação de estados quânticos na generalização de dualidades interferométricas em cenários de múltiplos caminhos

Abstract

Starting from the recoiling double slit gedanken experiment, protagonist of the debates between Einstein and Bohr, we study the main steps that led to the discussion of the complementarity between path information and interference visibility at intermediate domains, where each quantity is partially known. Trying to highlight the strategies of quantification of path knowledge, we emphasize the existence of two regimes of complementarity. The first regime, which leads to the formulation of Greenberger-Yasin duality, is based on predictive strategies. The second one, which leads to the formulation of Englert-Greenberger-Yasin duality (EGY), is based on the retrodiction of the path through the result of a measurement on an auxiliary system. In this second regime, we stress the point that the description of the auxiliary system through nonorthogonal quantum states is the essential ingredient in the derivation of EGY duality. Thus, the quantitative study of complementarity opens space for a close relationship with the strategies of discrimination of quantum states, which for a long time was mentioned in the literature only in a very subtle way. In addition, we also study recent works, which make use of a coherence quantifier and take important steps in obtaining interferometric dualities in a multipath scenario. At the end we present a preliminary form of generalization of these works in a three-way interferometer.