Pretty good state transfer in qubit chains—The Heisenberg Hamiltonian (original) (raw)

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 prime congruent to 1 modulo 4 or 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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