Related papers: Replica topological order in quantum mixed states …
Topological quantum memory can protect information against local errors up to finite error thresholds. Such thresholds are usually determined based on the success of decoding algorithms rather than the intrinsic properties of the mixed…
For closed quantum systems, topological orders are understood through the equivalence classes of ground states of gapped local Hamiltonians. The generalization of this conceptual paradigm to open quantum systems, however, remains elusive,…
Mixed-state phases of matter under local decoherence have recently garnered significant attention due to the ubiquitous presence of noise in current quantum processors. One of the key issues is understanding how topological quantum memory…
We develop an effective field theory characterizing the impact of decoherence on states with abelian topological order and on their capacity to protect quantum information. The decoherence appears as a temporal defect in the double…
We analyze the computational aspects of detecting topological order in a quantum many-body system. We contrast the widely used topological entanglement entropy with a recently introduced operational definition for topological order based on…
The unrivaled robustness of topologically ordered states of matter against perturbations has immediate applications in quantum computing and quantum metrology, yet their very existence poses a challenge to our understanding of phase…
The classification of topological phases of matter is fundamental to understand and characterize the properties of quantum materials. In this paper we study phases of matter in one-dimensional open quantum systems. We define two mixed…
We show how to generalize the concepts of identifying and classifying symmetry protected topological phases in 1D to the case of an arbitrary mixed state. The pure state concepts are reviewed using a concrete spin-1 model. For the mixed…
Quantum error correction (QEC) is crucial for realizing scalable quantum technologies, and topological quantum error correction (TQEC) has emerged as the most experimentally advanced paradigm of QEC. Existing homological and topological…
The discovery of topological order has revolutionized the understanding of quantum matter in modern physics and provided the theoretical foundation for many quantum error correcting codes. Realizing topologically ordered states has proven…
Quantum information can be protected from decoherence and other errors, but only if these errors are sufficiently rare. For quantum computation to become a scalable technology, practical schemes for quantum error correction that can…
Calculation of topological order parameters, such as the topological entropy and topological mutual information, are used to determine whether states possess topological order. Their calculation is expected to give reliable results when the…
Quantum critical phases are extended regions of phase space characterized by a diverging correlation length. By analogy, we define an information critical phase as an extended region of a mixed state phase diagram where the Markov length,…
We analyze surface codes, the topological quantum error-correcting codes introduced by Kitaev. In these codes, qubits are arranged in a two-dimensional array on a surface of nontrivial topology, and encoded quantum operations are associated…
Topological quantum field theories (TQFT) encode quantum correlations in topological features of spaces. In this work, we leverage this feature to explore how information encoded in TQFTs can be stored and retrieved in the presence of local…
We present a method of extracting information about the topological order from the ground state of a strongly correlated two-dimensional system computed with the infinite projected entangled pair state (iPEPS). For topologically ordered…
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 that two mixed states are in the same phase, as defined by their…
Certain pure-state symmetry-protected topological orders (SPT) can be used as a resource for transmitting quantum information. Here, we investigate the ability to transmit quantum information using decohered SPT states, and relate this…
We investigate the extension of pure-state symmetry protected topological phases to mixed-state regime with a strong U(1) and a weak $\mathbb{Z}_2$ symmetries in one-dimensional spin systems by the concept of quantum channels. We propose a…
Topological order has become a new paradigm to distinguish ground states of interacting many-body systems without conventional long-range order. Here we discuss possible extensions of this concept to density matrices describing statistical…