Quantum Information Processing

, Volume 13, Issue 7, pp 1607–1637 | Cite as

Quantum networks: anti-core of spin chains



The purpose of this paper is to exhibit a quantum network phenomenon—the anti-core—that goes against the classical network concept of congestion core. Classical networks idealized as infinite, Gromov hyperbolic spaces with least-cost path routing (and subject to a technical condition on the Gromov boundary) have a congestion core, defined as a subnetwork that routing paths have a high probability of visiting. Here, we consider quantum networks, more specifically spin chains, define the so-called maximum excitation transfer probability \(p_{\max }(i,j)\) between spin \(i\) and spin \(j\) and show that the central spin has among all other spins the lowest probability of being excited or transmitting its excitation. The anti-core is singled out by analytical formulas for \(p_{\mathrm{max}}(i,j)\), revealing the number theoretic properties of quantum chains. By engineering the chain, we further show that this probability can be made vanishingly small.


Quantum networks Spin chains Transfer probability Distance Gromov negatively curved networks  Anti-core 



This research was supported by ARO MURI Contract W911NF-11-1-0268 and by NSF Grant CNS NetSE 1017881.


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Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  1. 1.Department of Electrical Engineering & Department of MathematicsUniversity of Southern CaliforniaLos AngelesUSA
  2. 2.Computer Science & InformaticsCardiff UniversityCardiffUK
  3. 3.College of Science (Physics)Swansea UniversitySwanseaUK

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