  Quantum correlations between distant particles remain enigmatic since the
birth of quantum mechanics. Here we predict a novel kind of bound quantum state
in the simplest one-dimensional setup of two interacting particles in a box.
Paradoxically, two entangled particles become localized at the opposite edges
of the box even though their interactions at large distance should seemingly
play no role. Such states could be realized in the waveguide quantum
electrodynamics platform, where an array of superconducting qubits or cold
atoms is coupled to a waveguide. We demonstrate how long-range
waveguide-mediated couplings enable interaction-induced quantum states
separated by large distances. Similarly to Majorana fermions in the Kitaev
model, such bound state of distant photons is immune to short-range
interactions and could find applications in robust quantum information
processing.
