A-B and C-D each start as a fresh Bell pair |Φ+⟩ — A never meets C or D, D never meets A or B. The full 4-qubit state factors as |Φ+⟩AB⊗|Φ+⟩CD.
Re-expressed in the Bell basis of the middle nodes B,C, that state is an equal mix of all four A-D Bell states, each tied to a matching B-C outcome. A real joint (CNOT+H) measurement on B and C collapses A and D onto one Bell state — without A and D ever being physically brought together. That's a basic quantum repeater hop.
The 16-amplitude 4-qubit statevector — state prep, the Bell-measurement circuit, projective collapse and the final A/D measurement — is computed live from the linear algebra, same engine as the 2D version, rendered here as a 3D repeater network you can orbit.