**Launch your smart contract idea in just 4 days!**

by IsomorphismJune 19th, 2024

**Author:**

(1) Hiranmoy Pal, National Institute of Technology Rourkela, Odisha-769008, India.

Introduction, Acknowledgments and References

Quantum state transfer plays an important role in quantum information processing. The evolution of certain pair states in a quantum network with Heisenberg XY Hamiltonian depends only on the local structure of the network, and it remains unchanged even if the global structure is altered. All graphs with high-fidelity vertex state transfer may be considered as isomorphic branches of the graph underlying a large quantum network to exhibit high-fidelity pair state transfer. Among other graphs, one may construct infinite family of trees admitting perfect pair state transfer.

The research is funded by Science and Engineering Research Board (Project: SRG/2021/000522).

[1] E. Farhi and S. Gutmann, Quantum computation and decision trees, Phys. Rev. A 58, 915 (1998).

[2] M. Christandl, N. Datta, A. Ekert, and A. J. Landahl, Perfect state transfer in quantum spin networks, Phys. Rev. Lett. 92, 187902 (2004).

[3] S. Bose, A. Casaccino, S. Mancini, and S. Severini, Communication in XYZ all-to-all quantum networks with a missing link, Int. J. Quantum Inf. 7, 713 (2009).

[4] H. Pal, Laplacian state transfer on graphs with an edge perturbation between twin vertices, Discrete Math. 345, 112872 (2022).

[5] S. Bose, Quantum communication through an unmodulated spin chain, Phys. Rev. Lett. 91, 207901 (2003).

[6] Q. Chen and C. Godsil, Pair state transfer, Quantum Inf. Process. 19, 321 (2020).

[7] M. Baˇsi´c, Characterization of quantum circulant networks having perfect state transfer, Quantum Inf. Process. 12, 345 (2013).

[8] H. Pal and B. Bhattacharjya, Pretty good state transfer on circulant graphs, Electron. J. Combin. 24, Paper No. 2.23, 13 (2017).

[9] C. Godsil, S. Kirkland, S. Severini, and J. Smith, Number-theoretic nature of communication in quantum spin systems, Phys. Rev. Lett. 109, 050502 (2012).

[10] D. Cvetkovi´c, P. Rowlinson, and S. Simi´c, An introduction to the theory of graph spectra, London Mathematical Society Student Texts, Vol. 75 (Cambridge University Press, Cambridge, 2010) pp. xii+364.

This paper is available on arxiv under CC BY 4.0 DEED license.

L O A D I N G

. . . comments & more!

. . . comments & more!