Quantum networks: anti-core of spin chains

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 $$p_{\max }(i,j)$$ p max ( i , j ) between spin $$i$$ i and spin $$j$$ 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 $$p_{\mathrm{max}}(i,j)$$ p 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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Quantum Information Processing Springer Journals

Quantum networks: anti-core of spin chains

, Volume 13 (7) – May 24, 2014
31 pages

/lp/springer_journal/quantum-networks-anti-core-of-spin-chains-o4x4dzzDmr
Publisher
Springer Journals
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/s11128-014-0755-5
Publisher site
See Article on Publisher Site

Abstract

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 $$p_{\max }(i,j)$$ p max ( i , j ) between spin $$i$$ i and spin $$j$$ 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 $$p_{\mathrm{max}}(i,j)$$ p 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.

Journal

Quantum Information ProcessingSpringer Journals

Published: May 24, 2014

References

• Scaled Gromov hyperbolic graphs
Jonckheere, E; Lohsoonthorn, P; Bonahon, F

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