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Erschienen in:
01.07.2014
Quantum networks: anti-core of spin chains
Erschienen in: Quantum Information Processing | Ausgabe 7/2014
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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 \(p_{\max }(i,j)\) 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.