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Quantum correlations between distant particles remain enigmatic since thebirth of quantum mechanics. Here we predict a novel kind of bound quantum statein the simplest one-dimensional setup of two interacting particles in a box.Paradoxically, two entangled particles become localized at the opposite edgesof the box even though their interactions at large distance should seeminglyplay no role. Such states could be realized in the waveguide quantumelectrodynamics platform, where an array of superconducting qubits or coldatoms is coupled to a waveguide. We demonstrate how long-rangewaveguide-mediated couplings enable interaction-induced quantum statesseparated by large distances. Similarly to Majorana fermions in the Kitaevmodel, such bound state of distant photons is immune to short-rangeinteractions and could find applications in robust quantum informationprocessing.

Bound state of distant photons in waveguide quantum electrodynamics