Perfect state transfer on quotient graphs

Authors:
Rachel Bachman;Eric Fredette;Jessica Fuller;Michael Landry;Michael Opperman;Christino Tamon;Andrew Tollefson
Affiliations:
Department of Mathematics, Clarkson University, Potsdam, NY;Department of Mathematics, Clarkson University, Potsdam, NY;Department of Mathematics and Computer Science, Seton Hall University, South Orange, NJ;Department of Mathematics, University of California at Berkeley, Berkeley, CA;Department of Mathematics, Clarkson University, Potsdam, NY;Department of Computer Science, Clarkson University, Potsdam, NY;Department of Mathematics, University of Nevada at Reno, Reno, NV
Venue:
Quantum Information & Computation
Year:
2012

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Abstract

We prove new results on perfect state transfer of quantum walks on quotient graphs. Since a graph G has perfect state transfer if and only if its quotient G/π, under any equitable partition π, has perfect state transfer, we exhibit graphs with perfect state transfer between two vertices but which lack automorphism swapping them. This answers a question of Godsil (Discrete Mathematics 312(1):129-147, 2011). We also show that the Cartesian product of quotient graphs kGk/πk is isomorphic to the quotient graph kGk/π, for some equitable partition π. This provides an algebraic description of a construction due to Feder (Physical Review Letters 97, 180502, 2006) which is based on many-boson quantum walk.