Pretty good quantum fractional revival in paths and cycles

Ada Chan,Mark Kempton,Or Eisenberg,Gabor Lippner,Whitney Drazen

doi:10.5802/alco.189

Abstract

Pretty good quantum fractional revival in paths and cycles

Highlights

Tools and methods from algebraic and spectral graph theory have found important application in quantum information theory regarding the transfer of information through a quantum network
Given a graph that represents a network of interacting qubits, information transfer in this network can be modeled by a quantum walk on the graph
The study of perfect state transfer in graphs was initiated by Bose in 2003 [3], and since the problem has attracted considerable attention, both from the quantum information community and from the algebraic graph theory community

Summary

Introduction

Tools and methods from algebraic and spectral graph theory have found important application in quantum information theory regarding the transfer of information through a quantum network. The study of perfect state transfer in graphs was initiated by Bose in 2003 [3], and since the problem has attracted considerable attention, both from the quantum information community and from the algebraic graph theory community (see for instance [8, 15, 16, 19, 20, 24] and references therein). It has been shown that in simple, unweighted graphs, perfect state transfer is very difficult to achieve and occurs only rarely [16]. In simple unweighted path graphs, perfect state transfer occurs only in paths of length 2 and 3, and not in paths of any higher length [15].

Pretty good fractional revival

Findings

Cycles