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arXiv · 1608.04722

Pretty Good State Transfer in Qubit Chains - The Heisenberg Hamiltonian

Leonardo Banchi·Gabriel Coutinho·Chris Godsil·Simone Severini
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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 j-th and (n-j+1)-th position 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.

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Leonardo Banchi, Gabriel Coutinho, Chris Godsil, Simone Severini. 2016-08-16. Pretty Good State Transfer in Qubit Chains - The Heisenberg Hamiltonian. https://doi.org/10.1063/1.4978327

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