Number-theoretic nature of communication in quantum spin chains

Details Number-theoretic nature of communication in quantum spin chains Number-theoretic nature of communication in quantum spin chains

2012-01-23

arxiv.org/abs/1201.4822v1

Physics

Quantum Physics

9 pages, 1 EPS figure

Scientific paper

The last decade has witnessed a 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 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 XY Hamiltonian) that permit the transfer with fidelity arbitarily 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 dynamics for reinterpreting questions about the arithmetic structure of integers, and in this case, primality.

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