Holographic View of Mixed-State Symmetry-Protected Topological Phases in Open Quantum Systems

Journal Article · Tue May 20 00:00:00 EDT 2025 · PRX Quantum

DOI:https://doi.org/10.1103/PRXQuantum.6.020333· OSTI ID:2567835

Sun, Shijun; Zhang, Jian-Hao; Bi, Zhen; You, Yizhi

We establish a holographic duality between $d$ -dimensional mixed-state symmetry-protected topological (mSPT) phases and $(d+1)$ -dimensional subsystem symmetry-protected topological (SSPT) states. Specifically, we show that the reduced density matrix of the boundary layer of a $(d+1)$ -dimensional SSPT state with subsystem symmetry $\mathcal{S}$ and global symmetry $\mathcal{G}$ corresponds to a $d$ -dimensional mSPT phase with strong $\mathcal{S}$ and weak $\mathcal{G}$ symmetries. Conversely, we demonstrate that the wave function of an SSPT state can be constructed by replicating the density matrix of the corresponding lower-dimensional mSPT phase. This mapping links the density matrix in lower dimensions to the entanglement properties of higher-dimensional wave functions, providing an approach for analyzing nonlinear quantities and quantum information metrics in mixed-state systems. Our duality offers a new perspective for studying intrinsic mSPT phases that are unique to open quantum systems, without pure-state analogues. We show that strange correlators and twisted Rényi- $N$ correlators can diagnose these nontrivial phases and we explore their connection to strange correlators in pure-state SSPT phases. Furthermore, we discuss several implications of this holographic duality, including a method for preparing intrinsic mSPT phases through the duality.

Published by the American Physical Society 2025

• Sponsoring Organization: USDOE
• Grant/Contract Number: SC0024324
• OSTI ID: 2567835
• Journal Information: PRX Quantum, Journal Name: PRX Quantum Journal Issue: 2 Vol. 6; ISSN 2691-3399; ISSN PQRUAG
• Publisher: American Physical Society
• Country of Publication: United States
• Language: English