On the connection between complementarity and uncertainty principles in the Mach?Zehnder interferometric setting

BOSYK, G. M.; PORTESI, M.; HOLIK, F.; PLASTINO, A.L.

PHYSICA SCRIPTA - (Print)

IOP PUBLISHING LTD

Lugar: Londres; Año: 2013 vol. 87 p. 650021 - 650027

0031-8949

We revisit the connection between the complementarity and uncertainty principles of quantum mechanics within the framework of Mach?Zehnder interferometry. We focus our attention on the trade-off relation between complementary path information and fringe visibility. This relation is equivalent to the uncertainty relation of Schrödinger and Robertson for a suitably chosen pair of observables. We show that it is equivalent as well to the uncertainty inequality provided by Landau and Pollak. We also study the relationship of this trade-off relation with a family of entropic uncertainty relations based on R´enyi entropies. There is no equivalence in this case, but the different values of the entropic parameter do define regimes that provides us with a tool to discriminate between non-trivial states of minimum uncertainty. The existence of such regimes agrees with previous results of Luis (2011 Phys. Rev. A 84 034101), although their meaning was not sufficiently clear. We discuss the origin of these regimes with the intention of gaining a deeper understanding of entropic measures.