Quantum state transfer between twins in weighted graphs

Abstract

Twin vertices in simple unweighted graphs are vertices that have the same neighbours and, in the case of weighted graphs with possible loops, the corresponding incident edges have equal weights. In this paper, we explore the role of twin vertices in quantum state transfer. In particular, we provide characterizations of periodicity, perfect state transfer, and pretty good state transfer between twin vertices in a weighted graph with respect to its adjacency, Laplacian and signless Laplacian matrices. As an application, we provide characterizations of all simple unweighted double cones on regular graphs that exhibit periodicity, perfect state transfer, and pretty good state transfer.

arXiv comment23 pages, 1 figure

References in corpus (15)

• Quantum Communication Through an Unmodulated Spin Chain
• Quantum Computation and Decision Trees
• Perfect state transfer in quantum spin networks
• Perfect Transfer of Arbitrary States in Quantum Spin Networks
• A Review of Perfect State Transfer and its Application as a Constructive Tool
• Quantum walks on general graphs
• Number-Theoretic Nature of Communication in Quantum Spin Systems
• Perfect state transfer in cubelike graphs
• The Basics of Perfect Communication through Quantum Networks
• Perfect state transfer on distance-regular graphs and association schemes
• Almost perfect state transfer in quantum spin chains
• Pretty Good State Transfer in Qubit Chains - The Heisenberg Hamiltonian
• No Laplacian Perfect State Transfer in Trees
• Perfect quantum state transfer using Hadamard diagonalizable graphs
• Spin systems dynamics and faults detection in threshold networks