Characterizing graph symmetries through quantum Jensen-Shannon divergence

Rossi, Luca, Torsello, Andrea, Hancock, Edwin R. and Wilson, Richard C. (2013). Characterizing graph symmetries through quantum Jensen-Shannon divergence. Physical Review E, 88 (3),

Abstract

In this paper we investigate the connection between quantum walks and graph symmetries. We begin by designing an experiment that allows us to analyze the behavior of the quantum walks on the graph without causing the wave function collapse. To achieve this, we base our analysis on the recently introduced quantum Jensen-Shannon divergence. In particular, we show that the quantum Jensen-Shannon divergence between the evolution of two quantum walks with suitably defined initial states is maximum when the graph presents symmetries. Hence, we assign to each pair of nodes of the graph a value of the divergence, and we average over all pairs of nodes to characterize the degree of symmetry possessed by a graph.

Publication DOI: https://doi.org/10.1103/PhysRevE.88.032806
Divisions: Engineering & Applied Sciences
Uncontrolled Keywords: Condensed Matter Physics,Statistical and Nonlinear Physics,Statistics and Probability
Full Text Link: https://iris.un ... 49/phys_rev.pdf
Related URLs: http://www.scop ... tnerID=8YFLogxK (Scopus URL)
http://journals ... sRevE.88.032806 (Publisher URL)
Published Date: 2013-09-10
Authors: Rossi, Luca ( 0000-0002-6116-9761)
Torsello, Andrea
Hancock, Edwin R.
Wilson, Richard C.

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