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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| Format: | Article |
| Language: | English |
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American Physical Society
2025-05-01
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| 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. |
| format | Article |
| id | doaj-art-2ce7e3bda0cf41599d4f276eb43eada8 |
| institution | DOAJ |
| issn | 2691-3399 |
| language | English |
| publishDate | 2025-05-01 |
| publisher | American Physical Society |
| record_format | Article |
| series | PRX Quantum |
| 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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