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

Understand

We establish a holographic duality between d-dimensional mixed-state symmetry-protected topological phases (mSPTs) and (d+1)-dimensional subsystem symmetry-protected topological states (SSPTs).

• Specifically, we show that the reduced density matrix of the boundary layer of a (d+1)-dimensional SSPT with subsystem symmetry S and global symmetry G corresponds to a d-dimensional mSPT with strong S and weak G symmetries.
• Conversely, we demonstrate that the wavefunction of an SSPT can be constructed by replicating the density matrix of the corresponding lower-dimensional mSPT.
• This mapping links the density matrix in lower dimensions to the entanglement properties of higher-dimensional wavefunctions, providing an approach for analyzing nonlinear quantities and quantum information metrics in mixed-state systems.