title: Number-theoretic nature of communication in quantum spin systems.
abstract: The last decade has witnessed substantial interest in protocols for transferring information on networks of quantum mechanical objects. A variety of control methods and network topologies have been proposed, on the basis that transfer with perfect fidelity-i.e., deterministic and without information loss-is impossible through unmodulated spin chains with more than a few particles. Solving the original problem formulated by Bose [Phys. Rev. Lett. 91, 207901 (2003)], we determine the exact number of qubits in unmodulated chains (with an XY Hamiltonian) that permit transfer with a fidelity arbitrarily close to 1, a phenomenon called pretty good state transfer. We prove that this happens if and only if the number of nodes is n = p - 1, 2p - 1, where p is a prime, or n = 2(m) - 1. The result highlights the potential of quantum spin system dynamics for reinterpreting questions about the arithmetic structure of integers and, in this case, primality.
authors.affiliation: Combinatorics & Optimization, University of Waterloo, Canada.
authors.forename: Chris
authors.initials: C
authors.lastname: Godsil
authors.forename: Stephen
authors.initials: S
authors.lastname: Kirkland
authors.forename: Simone
authors.initials: S
authors.lastname: Severini
authors.forename: Jamie
authors.initials: J
authors.lastname: Smith