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 pmax(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 pmax(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.