Asymptotic behavior near maximal even-site X-decoherence

Determine the asymptotic behavior of the characteristic length and the associated strong-to-weak spontaneous symmetry-breaking correlations in the filtered one-dimensional cluster-state ASPT as the even-site X-decoherence strength approaches the maximal value p_x=1/2.

Background

The paper studies an average symmetry-protected topological state obtained from the one-dimensional cluster state by even-site Z-decoherence, and then applies an additional symmetry-preserving even-site X-decoherence channel with strength p_x. The authors compare the ASPT purity-weighted string order with Renyi-2 ZZ correlations associated with strong-to-weak spontaneous symmetry breaking.

Numerical calculations show that the ZZ correlations become sharply enhanced as p_x approaches 1/2, but the system-size dependence is better described by a finite correlation length than by clear evidence of a finite-p_x phase transition. The extracted characteristic length grows rapidly near the maximal-decoherence limit, while the accessible system sizes are insufficient to establish its limiting or asymptotic behavior.

References

Rather, it is consistent with an increasingly large characteristic length as the maximal-decoherence limit $p_x=1/2$ is approached, although the available system sizes do not allow us to determine its asymptotic behavior.

— Fate of average symmetry-protected topological states under symmetry-preserving quantum operations  (2609.27530 - Kuno et al., 23 Sep 2026) in Section VI, subsection “Even-site X-decoherence channel”