Extended Data Fig. 1: Topological phase diagrams for varying chain lengths.

These panels show the calculated end-to-end gain \({\chi }_{{x}_{1}\to {x}_{N}}\) for finite open chains of length N = 4 (panel (a), corresponding to Fig. 3c), N = 10 (b), and N = 20 (c), as a function of phase φ and squeezing amplitude λ/J for J/γ = 5/16. As in Fig. 3c, the dashed lines depict the phase boundaries, determined by the structure (point gap and winding of origin) of the complex spectrum for an infinite chain under PBC. We recognize that the conditions for which the end-to-end gain exceeds unity align closely with the topological phase boundary that marks spectral winding of the origin. Slight deviations between those two are observed for smaller chains near φ = 0 and φ = π/2, and are thus associated with finite size effects. Still, the general structure of the phase diagram of the infinite chain is clearly recognized in the end-to-end gain for N = 4.