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

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 stat...

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Main Authors: Shijun Sun, Jian-Hao Zhang, Zhen Bi, Yizhi You
Format: Article
Language:English
Published: American Physical Society 2025-05-01
Series:PRX Quantum
Online Access:http://doi.org/10.1103/PRXQuantum.6.020333
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author Shijun Sun
Jian-Hao Zhang
Zhen Bi
Yizhi You
author_facet Shijun Sun
Jian-Hao Zhang
Zhen Bi
Yizhi You
author_sort Shijun Sun
collection DOAJ
description 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 S and global symmetry G corresponds to a d-dimensional mSPT phase with strong S and weak 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.
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spelling doaj-art-2ce7e3bda0cf41599d4f276eb43eada82025-08-20T03:08:13ZengAmerican Physical SocietyPRX Quantum2691-33992025-05-016202033310.1103/PRXQuantum.6.020333Holographic View of Mixed-State Symmetry-Protected Topological Phases in Open Quantum SystemsShijun SunJian-Hao ZhangZhen BiYizhi YouWe 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 S and global symmetry G corresponds to a d-dimensional mSPT phase with strong S and weak 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.http://doi.org/10.1103/PRXQuantum.6.020333
spellingShingle Shijun Sun
Jian-Hao Zhang
Zhen Bi
Yizhi You
Holographic View of Mixed-State Symmetry-Protected Topological Phases in Open Quantum Systems
PRX Quantum
title Holographic View of Mixed-State Symmetry-Protected Topological Phases in Open Quantum Systems
title_full Holographic View of Mixed-State Symmetry-Protected Topological Phases in Open Quantum Systems
title_fullStr Holographic View of Mixed-State Symmetry-Protected Topological Phases in Open Quantum Systems
title_full_unstemmed Holographic View of Mixed-State Symmetry-Protected Topological Phases in Open Quantum Systems
title_short Holographic View of Mixed-State Symmetry-Protected Topological Phases in Open Quantum Systems
title_sort holographic view of mixed state symmetry protected topological phases in open quantum systems
url http://doi.org/10.1103/PRXQuantum.6.020333
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AT zhenbi holographicviewofmixedstatesymmetryprotectedtopologicalphasesinopenquantumsystems
AT yizhiyou holographicviewofmixedstatesymmetryprotectedtopologicalphasesinopenquantumsystems