2012/01/31 by Chris Godsil, Stephen Kirkland, Simone Severini +1 · 3 citations
Computer Science · Mathematics · Physics and Astronomy · #Combinatorics #Computer science #Hamiltonian (control theory) #Mathematics #Physics #Quantum #Quantum Computing Algorithms and Architecture #Quantum Information and Cryptography #Quantum Mechanics and Applications #Quantum entanglement #Quantum information #Quantum information science #Quantum mechanics #Quantum network #Qubit #Spin (aerodynamics) #Topology (electrical circuits) #quant-ph
paper · pdf · doi:10.1103/physrevlett.109.050502
published as Phys. Rev. Lett. 109, 050502 (2012) · 6 pages, 1 EPS figure
openalex publication_date 2012/08/01 · arxiv created 2012/08/11 · arxiv updated 2012/08/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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.