×

zbMATH — the first resource for mathematics

Pretty good quantum state transfer in asymmetric graphs via potential. (English) Zbl 1417.05172
Summary: We construct infinite families of graphs in which pretty good state transfer can be induced by adding a potential to the nodes of the graph (i.e. adding a number to a diagonal entry of the adjacency matrix). Indeed, we show that given any graph with a pair of cospectral nodes, a simple modification of the graph, along with a suitable potential, yields pretty good state transfer between the nodes. This generalizes previous work, concerning graphs with an involution, to asymmetric graphs.

MSC:
05C75 Structural characterization of families of graphs
05C50 Graphs and linear algebra (matrices, eigenvalues, etc.)
PDF BibTeX XML Cite
Full Text: DOI arXiv
References:
[1] Bachman, R.; Fredette, E.; Fuller, J.; Landry, M.; Opperman, M.; Tamon, C.; Tollefson, A., Perfect state transfer on quotient graphs, Quantum Inf. Comput., 12, 3-4, 293-313, (2012) · Zbl 1256.81018
[2] Banchi, L.; Coutinho, G.; Godsil, C.; Severini, S., Pretty good state transfer in qubit chains – the heisenberg hamiltonian, J. Math. Phys., 58, 3, 032202, (2017) · Zbl 1359.81047
[3] Bose, S., Quantum communication through an unmodulated spin chain, Phys. Rev. Lett., 91, 20, 207901, (2003)
[4] Christandl, M.; Datta, N.; Ekert, A.; Landahl, A. J., Perfect state transfer in quantum spin networks, Phys. Rev. Lett., 92, 187902, (2004)
[5] Coutinho, G.; Guo, K.; van Bommel, C. M., Pretty good state transfer between internal nodes of paths, Quantum Inf. Comput., 17, 9-10, 825-830, (2017)
[6] C. Godsil, Graph spectra and quantum walks (2017) unpublished manuscript.
[7] Godsil, C., Algebraic Combinatorics, (1993), Chapman & Hall: Chapman & Hall New York · Zbl 0784.05001
[8] Godsil, C., State transfer on graphs, Discrete Math., 312, 1, 129-147, (2012) · Zbl 1232.05123
[9] C. Godsil, K. Guo, M. Kempton, G. Lippner, State transfer in strongly regular graphs with an edge perturbation (2017). ArXiv preprint: arxiv.org/pdf/1710.02181.pdf.
[10] Godsil, C.; Kirkland, S.; Severini, S.; Smith, J., Number-theoretic nature of communication in quantum spin systems, Phys. Rev. Lett., 109, 5, 050502, (2012)
[11] C. Godsil, J. Smith, Strongly cospectral vertices (2017). ArXiv preprint: arxiv.org/pdf/1709.07975.pdf.
[12] Horn, R. A.; Johnson, C. R., Matrix Analysis, (2013), Cambridge University Press: Cambridge University Press Cambridge · Zbl 1267.15001
[13] Kay, A., Perfect, efficient, state transfer and its applications as a constructive tool, Int. J. Quantum Inform., 8, 4, 641, (2010) · Zbl 1194.81046
[14] Kempton, M.; Lippner, G.; Yau, S.-T., Perfect state transfer on graphs with a potential, Quantum Inf. Comput., 17, 3, 303-327, (2017)
[15] Kempton, M.; Lippner, G.; Yau, S.-T., Pretty good quantum state transfer in symmetric spin networks via magnetic field, Quantum Inf. Process., 16, 9, 16:210, (2017) · Zbl 1382.81049
[16] C.M. van Bommel, A complete characterization of pretty good state transfer in paths (2016). ArXiv preprint: arxiv.org/pdf/1612.05603.pdf.
[17] Vinet, L.; Zhedanov, A., Almost perfect state transfer in quantum spin chains, Phys. Rev. A, 86, 052319, (2012)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.