We explore the effect of decoherence on many-body mixed states from a purification
perspective. Here, quantum channels map to unitary transformations acting on a purified …

We study the entanglement structure of topological orders subject to decoherence on the
bipartition boundary. Focusing on the toric codes in d space dimensions for d= 2, 3, 4, we …

We propose a tensor network approach known as the locally purified density operator
(LPDO) to investigate the classification and characterization of symmetry-protected …

Decoherence is a major obstacle to the preparation of topological order in noisy
intermediate-scale quantum devices. Here, we show that decoherence can also give rise to …

Depending on the coupling to the environment, symmetries of open quantum systems
manifest in two distinct forms, the strong and the weak. We study the spontaneous symmetry …

The effect of decoherence on topological order (TO) has been most deeply understood for
the toric code, the paragon of Abelian TOs. We show that certain non-Abelian TOs can be …

We introduce a class of intrinsic symmetry-protected topological mixed state (mSPT) in open
quantum systems that feature modulated symmetries, such as dipole and subsystem …

For quantum phases of Hamiltonian ground states, the energy gap plays a central role in
ensuring the stability of the phase as long as the gap remains finite. We propose Markov …

Topological orders in 2+ 1d are spontaneous symmetry-breaking (SSB) phases of 1-form
symmetries in pure states. The notion of symmetry is further enriched in the context of mixed …

Symmetry in mixed quantum states can manifest in two distinct forms: strong symmetry,
where each individual pure state in the quantum ensemble is symmetric with the same …