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Abstract

Short-range entangled topological phases that require certain symmetries for their existence, which are known as symmetry-protected topological (SPT) phases, are by now fairly well understood. In one-dimensional closed systems, their non-triviality is captured by the emergent edge states (or projective representations acting at the boundaries). However, one immediately realizes that naive generalization of this strategy fails for open quantum systems in which density operators are fundamental. Therefore, it is highly desirable to establish how to characterize SPT phases in open quantum systems not only from theoretical interest but also in view of experimental detections.

In this respect, several approaches have been proposed [1] so far. In this talk, we propose "operational" characterization using measurement-based quantum computation (MBQC) [2]. Remarkably, non-local correlation functions similar to the string order parameters quantify (symmetry-protected) topological nature of given mixed states [3]. We also discuss under which conditions SPT phases are stable against decoherence.

References
[1] C. de Groot, A. Turzillo, and N. Schuch, Quantum, 6, 856 (2022).
[2] R. Raussendorf and H.J. Briegel, Phys.Rev.Lett. 86, 5188 (2001); G.K. Brennen and K. Miyake, Phys.Rev.Lett.101, 010502 (2008).
[3] R. Masui and K. Totsuka, Phys.Rev.B 112, 085108 (2025).