Godsil, C;
Kirkland, S;
Severini, S;
Smith, J;
(2012)
Number-theoretic nature of communication in quantum spin systems.
Physical Review Letters
, 109
(5)
, Article 050502. 10.1103/PhysRevLett.109.050502.
Preview |
PDF
1345894.pdf Download (121kB) |
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.
Type: | Article |
---|---|
Title: | Number-theoretic nature of communication in quantum spin systems. |
Location: | United States |
Open access status: | An open access version is available from UCL Discovery |
DOI: | 10.1103/PhysRevLett.109.050502 |
Publisher version: | http://dx.doi.org/10.1103/PhysRevLett.109.050502 |
Language: | English |
Additional information: | © 2012 American Physical Society |
UCL classification: | UCL UCL > Provost and Vice Provost Offices > UCL BEAMS UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Engineering Science UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Engineering Science > Dept of Computer Science |
URI: | https://discovery.ucl.ac.uk/id/eprint/1345894 |
Archive Staff Only
View Item |