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Pretty good state transfer in qubit chains-The Heisenberg Hamiltonian

Banchi, L; Coutinho, G; Godsil, C; Severini, S; (2017) Pretty good state transfer in qubit chains-The Heisenberg Hamiltonian. Journal of Mathematical Physics , 58 (3) 10.1063/1.4978327. Green open access

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Abstract

Pretty good state transfer in networks of qubits occurs when a continuous-time quantum walk allows the transmission of a qubit state from one node of the network to another, with fidelity arbitrarily close to 1. We prove that in a Heisenberg chain with n qubits, there is pretty good state transfer between the nodes at the jth and (n − j + 1)th positions if n is a power of 2. Moreover, this condition is also necessary for j = 1. We obtain this result by applying a theorem due to Kronecker about Diophantine approximations, together with techniques from algebraic graph theory.

Type: Article
Title: Pretty good state transfer in qubit chains-The Heisenberg Hamiltonian
Open access status: An open access version is available from UCL Discovery
DOI: 10.1063/1.4978327
Publisher version: http://doi.org/10.1063/1.4978327
Additional information: This version is the author accepted manuscript. For information on re-use, please refer to the publisher’s terms and conditions.
UCL classification: UCL > Provost and Vice Provost Offices
UCL > Provost and Vice Provost Offices > UCL BEAMS
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Engineering Science
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Engineering Science > Dept of Computer Science
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences
URI: http://discovery.ucl.ac.uk/id/eprint/1526394
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