Number-Theoretic Nature of Communication in Quantum Spin Systems

作者：Godsil Chris^*; Kirkland Stephen; Severini Simone; Smith Jamie

来源：Physical Review Letters, 2012, 109(5): 050502.

DOI：10.1103/PhysRevLett.109.050502

• Control methods
• Network topology
• Primality
• Quantum mechanical
• Quantum spin systems
• Spin chains
• State transfer

The last decade has witnessed substantial interest in protocols for transferring information on networks of quantum mechanical objects. Avariety 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.

• 出版日期2012-8-1