Wang, Jing; Liu, Xiaogang State transfers in vertex complemented coronas. (English) Zbl 1497.05164 Discrete Appl. Math. 321, 165-178 (2022). Summary: In this paper, we study the existence of perfect state transfer and pretty good state transfer in vertex complemented coronas. We prove that perfect state transfer in vertex complemented coronas is extremely rare. In contrast, we give sufficient conditions for vertex complemented coronas to have pretty good state transfer. MSC: 05C50 Graphs and linear algebra (matrices, eigenvalues, etc.) 05C40 Connectivity 81P45 Quantum information, communication, networks (quantum-theoretic aspects) 81P68 Quantum computation 15A18 Eigenvalues, singular values, and eigenvectors Keywords:perfect state transfer; pretty good state transfer; vertex complemented corona PDFBibTeX XMLCite \textit{J. Wang} and \textit{X. Liu}, Discrete Appl. Math. 321, 165--178 (2022; Zbl 1497.05164) Full Text: DOI arXiv References: [1] Ackelsberg, E.; Brehm, Z.; Chan, A.; Mundinger, J.; Tamon, C., Quantum state transfer in coronas, Electron. J. Combin., 24, 2 (2017), #P2.24 · Zbl 1364.05044 [2] Angeles-Canul, R. J.; Norton, R. M.; Opperman, M. C.; Paribello, C. C.; Russell, M. C.; Tamon, C., Perfect state transfer, integral circulants, and join of graphs, Quantum Inf. Comput., 10, 3 & 4, 0325-0342 (2010) · Zbl 1236.81049 [3] Bašić, M., Characterization of quantum circulant networks having perfect state transfer, Quantum Inf. Process., 12, 1, 345-364 (2013) · Zbl 1309.81043 [4] Bašić, M.; Petković, M. D., Some classes of integral circulant graphs either allowing or not allowing perfect state transfer, Appl. Math. Lett., 22, 1609-1615 (2009) · Zbl 1171.05354 [5] Bose, S., Quantum communication through an unmodulated spin chain, Phys. Rev. Lett., 91, 20, Article 207901 pp. (2003) [6] Brouwer, A. E.; Cohen, A. M.; Neumaier, A., Distance-Regular Graphs (1989), Springer-Verlag: Springer-Verlag Berlin · Zbl 0747.05073 [7] Cao, X.; Chen, B.; Ling, S., Perfect state transfer on cayley graphs over dihedral groups: The non-normal case, Electron. J. Combin., 27, 2 (2020), #P2.28 · Zbl 1441.05099 [8] Cao, X.; Feng, K., Perfect state transfer on Cayley graphs over dihedral groups, Linear Multilinear Algebra, 69, 2, 343-360 (2021) · Zbl 1459.05117 [9] Cao, X.; Wang, D.; Feng, K., Pretty good state transfer on Cayley graphs over dihedral groups, Discrete Math., 343, 1, Article 111636 pp. (2020) · Zbl 1429.05121 [10] Cheung, W.-C.; Godsil, C., Perfect state transfer in cubelike graphs, Linear Algebra Appl., 435, 2468-2474 (2011) · Zbl 1222.05150 [11] Christandl, M.; Datta, N.; Dorlas, T.; Ekert, A.; Kay, A.; Landahl, A., Perfect transfer of arbitrary states in quantum spin networks, Phys. Rev. A, 71, Article 032312 pp. (2005) [12] Christandl, M.; Datta, N.; Ekert, A.; Landahl, A., Perfect state transfer in quantum spin networks, Phys. Rev. Lett., 92, 18, Article 187902 pp. (2004) [13] Coutinho, G., Quantum State Transfer in Graphs (2014), University of Waterloo, (Ph.D. thesis) [14] Coutinho, G., Spectrally extremal vertices, strong cospectrality and state transfer, Electron. J. Combin., 23, 1 (2016), #P1.46 · Zbl 1333.05179 [15] Coutinho, G.; Godsil, C.; Guo, K.; Vanhove, F., Perfect state transfer on distance-regular graphs and association schemes, Linear Algebra Appl., 478, 108-130 (2015) · Zbl 1312.05147 [16] Coutinho, G.; Liu, H., No Laplacian perfect state transfer in trees, SIAM J. Discrete Math., 29, 4, 2179-2188 (2015) · Zbl 1327.05202 [17] Cui, S.; Tian, G., The spectrum and the signless Laplacian spectrum of coronae, Linear Algebra Appl., 437, 1692-1703 (2012) · Zbl 1247.05135 [18] Fan, X.; Godsil, C., Pretty good state transfer on double stars, Linear Algebra Appl., 438, 5, 2346-2358 (2013) · Zbl 1258.05069 [19] Farhi, E.; Gutmann, S., Quantum computation and decision trees, Phys. Rev. A, 58, 2, 915-928 (1998) [20] Gayathri, M., Spectra of Graphs Constructed By Various New Graph Operations (2020), The Gandhigram Rural Institute, (Ph.D. thesis) [21] Godsil, C., Periodic graphs, Electron. J. Combin., 18, 1 (2011), #P23 · Zbl 1213.05166 [22] Godsil, C., State transfer on graphs, Discrete Math., 312, 1, 129-147 (2012) · Zbl 1232.05123 [23] Godsil, C., When can perfect state transfer occur?, Electron. J. Linear Algebra, 23, 877-890 (2012) · Zbl 1253.05093 [24] Godsil, C.; Kirkland, S.; Severini, S.; Smith, J., Number-theoretic nature of communication in quantum spin systems, Phys. Rev. Lett., 109, 5, Article 050502 pp. (2012) [25] Hardy, G. H.; Wright, E. M., An Introduction to the Theory of Numbers (2000), Oxford University Press [26] Li, Y.; Liu, X.; Zhang, S.; Zhou, S., Perfect state transfer in NEPS of complete graphs, Discrete Appl. Math., 289, 98-114 (2021) · Zbl 1454.81095 [27] Liu, X.; Zhang, Z., Spectra of subdivision-vertex join and subdivision-edge join of two graphs, Bull. Malays. Math. Sci. Soc., 42, 15-31 (2019) · Zbl 1406.05063 [28] McLeman, C.; McNicholas, E., Spectra of coronae, Linear Algebra Appl., 435, 998-1007 (2011) · Zbl 1221.05239 [29] Meyer, C. D., Matrix Analysis and Applied Linear Algebra (2000), Siam: Siam Philadelphia · Zbl 0962.15001 [30] Pal, H., More circulant graphs exhibiting pretty good state transfer, Discrete Math., 341, 4, 889-895 (2018) · Zbl 1380.05124 [31] Pal, H.; Bhattacharjya, B., Perfect state transfer on NEPS of the path on three vertices, Discrete Math., 339, 831-838 (2016) · Zbl 1327.05325 [32] Pal, H.; Bhattacharjya, B., Perfect state transfer on gcd-graphs, Linear Multilinear Algebra, 65, 11, 2245-2256 (2017) · Zbl 1387.05070 [33] Pal, H.; Bhattacharjya, B., Pretty good state transfer on circulant graphs, Electron. J. Combin., 24, 2 (2017), #P2.23 · Zbl 1364.05027 [34] Pal, H.; Bhattacharjya, B., Pretty good state transfer on some NEPS, Discrete Math., 340, 4, 746-752 (2017) · Zbl 1355.05159 [35] Richards, I., An application of galois theory to elementary arithmetic, Adv. Math., 13, 3, 268-273 (1974) · Zbl 0292.12002 [36] Tan, Y.; Feng, K.; Cao, X., Perfect state transfer on abelian Cayley graphs, Linear Algebra Appl., 563, 331-352 (2019) · Zbl 1403.05066 [37] Thongsomnuk, I.; Meemark, Y., Perfect state transfer in unitary Cayley graphs and gcd-graphs, Linear Multilinear Algebra, 67, 1, 39-50 (2019) · Zbl 1429.05094 [38] Zhang, F., The Schur Complement and its Applications (2005), Springer: Springer New York · Zbl 1075.15002 [39] Zheng, S.; Liu, X.; Zhang, S., Perfect state transfer in NEPS of some graphs, Linear Multilinear Algebra, 68, 8, 1518-1533 (2020) · Zbl 1448.05136 [40] Zhou, J.; Bu, C., State transfer and star complements in graphs, Discrete Appl. Math., 176, 130-134 (2014) · Zbl 1297.05154 [41] Zhou, J.; Bu, C.; Shen, J., Some results for the periodicity and perfect state transfer, Electron. J. Combin., 18, 1 (2011), #P184 · Zbl 1229.05205 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. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.