Information transfer fidelity in spin networks and ring-based quantum routers

Information transfer fidelity in spin networks and ring-based quantum routers Spin networks are endowed with an information transfer fidelity (ITF), which defines an absolute upper bound on the probability of transmission of an excitation from one spin to another. The ITF is easily computable, but the bound can be reached asymptotically in time only under certain conditions. General conditions for attainability of the bound are established, and the process of achieving the maximum transfer probability is given a dynamical model, the translation on the torus. The time to reach the maximum probability is estimated using the simultaneous Diophantine approximation, implemented using a variant of the Lenstra–Lenstra–Lovász (LLL) algorithm. For a ring with uniform couplings, the network can be made into a metric space by defining a distance (satisfying the triangle inequality) that quantifies the lack of transmission fidelity between two nodes. It is shown that transfer fidelities and transfer times can be improved significantly by means of simple controls taking the form of nondynamic, spatially localized bias fields, opening up the possibility for intelligent design of spin networks and dynamic routing of information encoded in them, while being more flexible than engineering fixed couplings to favor some transfers, and less demanding than control schemes requiring fast dynamic controls. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Quantum Information Processing Springer Journals

Information transfer fidelity in spin networks and ring-based quantum routers

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Publisher
Springer US
Copyright
Copyright © 2015 by The Author(s)
Subject
Physics; Quantum Information Technology, Spintronics; Quantum Computing; Data Structures, Cryptology and Information Theory; Quantum Physics; Mathematical Physics
ISSN
1570-0755
eISSN
1573-1332
D.O.I.
10.1007/s11128-015-1136-4
Publisher site
See Article on Publisher Site

Abstract

Spin networks are endowed with an information transfer fidelity (ITF), which defines an absolute upper bound on the probability of transmission of an excitation from one spin to another. The ITF is easily computable, but the bound can be reached asymptotically in time only under certain conditions. General conditions for attainability of the bound are established, and the process of achieving the maximum transfer probability is given a dynamical model, the translation on the torus. The time to reach the maximum probability is estimated using the simultaneous Diophantine approximation, implemented using a variant of the Lenstra–Lenstra–Lovász (LLL) algorithm. For a ring with uniform couplings, the network can be made into a metric space by defining a distance (satisfying the triangle inequality) that quantifies the lack of transmission fidelity between two nodes. It is shown that transfer fidelities and transfer times can be improved significantly by means of simple controls taking the form of nondynamic, spatially localized bias fields, opening up the possibility for intelligent design of spin networks and dynamic routing of information encoded in them, while being more flexible than engineering fixed couplings to favor some transfers, and less demanding than control schemes requiring fast dynamic controls.

Journal

Quantum Information ProcessingSpringer Journals

Published: Oct 8, 2015

References

  • Quantum networks: the anti-core of spin chains
    Jonckheere, E; Schirmer, S; Langbein, F
  • Symmetry and controllability for spin networks with a single-node control
    Wang, X; Pemberton-Ross, P; Schirmer, SG
  • Distribution of eigenvalues of real symmetric palindromic Toeplitz matrices and circulant matrices
    Massey, A; Miller, SJ; Sinsheimer, J

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