FellowRNDr., PhD. Daniel Reitzner
Project NameQuantum Walks and Incompatibility
Host organisationInstitute of Physics
Duration of the project07.04.2015 - 06.04.2018

Abstract
The project focuses on two seemingly different topics. First addressed topic are the scattering properties of quantum walks on different graph structures. Using such scatterings we aim to efficiently detect specific characteristics of graphs as well to be able to design such graphs where the detection of the characteristics is possible and leads to advantageous behavior compared to classical approaches. Second part of the topic is to address the decoherence in the quantum-walks algorithms and assess their efficiency under such conditions. Second addressed topic is incompatibility of quantum measurements as a characteristic effect not only in the quantum theory but also in the whole hierarchy of statistical theories. The aim is to use this knowledge to design testable boundaries based on incompatibility that would distinguish quantum theory from the other theories (not only from the classical). The fusion of the two topics in the future shall be the description of incompatibility of quantum measurements in scatterings of quantum walkers on graph structures with possible use for the distinguishing the quantum theory from other theories.

Project Summary with Interim Results

The project consists of two separate parts, one on quantum walks (split into scatterings and decoherence questions) and the second one on quantum incompatibility.

In the first year of the project we addressed the issue of the decoherence in quantum walks, i.e. how are the applications of quantum walks affected by decoherence on given network. One partial result in this direction is that decoherence in quantum searches rather quickly destroys its efficiency up to few extra cases. This is, however, done only for a specific task related to Grover quantum search. The second result is the detection of extraneous edges, which might be considered as a leakage in the network. This result is still preliminary.

Objective on quantum incompatibility aimed this year at describing a general degree of incompatibility necessary for considering quantum incompatibility as a resource in quantum applications. This point has been addressed fully with additional results of providing a generalized Tsirelson bound. Further additional results, not planned within the project, but relating to the objective, were the expansion of the degree of incompatibility on measurements on evolutions and the description of dynamical effects on incompatibility.