Open system quantum dynamics can generate a variety of long-range entangled mixed
states, yet it has been unclear in what sense they constitute phases of matter. To establish …

We propose a general framework for studying two-dimensional (2D) topologically ordered
states subject to local correlated errors and show that the resulting mixed state can display …

Passive error correction protects logical information forever (in the thermodynamic limit) by
updating the system based only on local information and few-body interactions. A …

We provide a systematic framework for constructing generic models of nonequilibrium
quantum dynamics with a target stationary (mixed) state. Our framework identifies (almost) …

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 …

We present a family of local quantum channels whose steady states exhibit stable mixed-
state symmetry-protected topological (SPT) order. Motivated by recent experimental …

The interplay of symmetry and topology in quantum many-body mixed states has recently
garnered significant interest. In a phenomenon not seen in pure states, mixed states can …

Several quantum hardware platforms, while being unable to perform fully fault-tolerant
quantum computation, can still be operated as analogue quantum simulators for addressing …

In this paper, we develop a systematic approach to characterize the't Hooft anomaly in open
quantum systems. Owing to nontrivial couplings to the environment, symmetries in such …

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 …