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Open Quantum Systems Decoherence Quantum State Preparation Representation Quantum Simulation Entanglement Theory Quantum Correlations

When can perfect state transfer occur?

arXiv

Authors: Chris Godsil

Year

2010

Paper ID

10620

Status

Preprint

Abstract Read

~2 min

Abstract Words

148

Citations

N/A

Abstract

Let X be a graph on n vertices with with adjacency matrix A and let H(t) denote the matrix-valued function exp(iAt). If u and v are distinct vertices in X, we say perfect state transfer from u to v occurs if there is a time τ such that |H(τ)_u,v| = 1. Our chief problem is to characterize the cases where perfect state transfer occurs. We show that if perfect state transfer does occur in a graph, then the spectral radius is an integer or a quadratic irrational; using this we prove that there are only finitely many graphs with perfect state transfer and with maximum valency at most 4K4. We also show that if perfect state transfer from u to v occurs, then the graphs Xsetminus u and Xsetminus v are cospectral and any automorphism of X that fixes u must fix v (and conversely).

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This paper contributes to the Quantum Simulation research area in the Quantum Articles archive.
It adds a 2010 reference point for readers tracking recent quantum research.
Let X be a graph on n vertices with with adjacency matrix A and let H(t) denote the matrix-valued function exp(iAt).

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References & Citation Signals

[1] DOI https://doi.org/arXiv:1011.0231 [2] arXiv https://arxiv.org/abs/1011.0231 [3] Publisher https://arxiv.org/abs/1011.0231

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