Mixed-state long-range order and criticality from measurement and feedback

Abstract

We propose a general framework for using local measurements, local unitaries, and non-local classical communication to construct quantum channels which can efficiently prepare mixed states with long-range quantum order or quantum criticality. As an illustration, symmetry-protected topological (SPT) phases can be universally converted into mixed-states with long-range entanglement, which can undergo phase transitions with quantum critical correlations of local operators and a logarithmic scaling of the entanglement negativity, despite coexisting with volume-law entropy. Within the same framework, we present two applications using fermion occupation number measurement to convert (i) spinful free fermions in one dimension into a quantum-critical mixed state with enhanced algebraic correlations between spins and (ii) Chern insulators into a mixed state with critical quantum correlations in the bulk. The latter is an example where mixed-state quantum criticality can emerge from a gapped state of matter in constant depth using local quantum operations and non-local classical communication.

arXiv comment25 pages, 11 figures; updated to the published version

References in corpus (45)

• Mixed State Entanglement and Quantum Error Correction
• Anyons in an exactly solved model and beyond
• Separability Criterion for Density Matrices
• A computable measure of entanglement
• Unpaired Majorana fermions in quantum wires
• Separability of Mixed States: Necessary and Sufficient Conditions
• Entanglement Entropy and Quantum Field Theory
• Persistent entanglement in arrays of interacting particles
• Quantum Spin Liquids
• Geometric and Renormalized Entropy in Conformal Field Theory
• The logarithmic negativity: A full entanglement monotone that is not convex
• Quantum Spin Liquid States
• Majorana fermions in a tunable semiconductor device
• Classification of Gapped Symmetric Phases in 1D Spin Systems
• Entanglement monotones
• Lieb-Robinson bounds and the generation of correlations and topological quantum order
• Complete classification of 1D gapped quantum phases in interacting spin systems
• Detection of Symmetry Protected Topological Phases in 1D
• A comparison of entanglement measures
• Symmetry-protected topological orders for interacting fermions -- Fermionic topological nonlinear $\sigma$ models and a special group supercohomology theory
• Entanglement negativity in extended systems: A field theoretical approach
• A no-go theorem for a two-dimensional self-correcting quantum memory based on stabilizer codes
• Three-spin interactions in optical lattices and criticality in cluster Hamiltonians
• Symmetry protected topological phases from decorated domain walls
• Phase Structure of 1d Interacting Floquet Systems I: Abelian SPTs
• Long-range quantum entanglement in noisy cluster states
• Topological Order at Non-zero Temperature
• Gapless Symmetry Protected Topological Order
• Measurement as a shortcut to long-range entangled quantum matter
• Hierarchy of topological order from finite-depth unitaries, measurement and feedforward
• Identifying phases of quantum many-body systems that are universal for quantum computation
• Creation, manipulation, and detection of Abelian and non-Abelian anyons in optical lattices
• Quantum Circuits assisted by LOCC: Transformations and Phases of Matter
• Foliated Quantum Codes
• Detecting Topological Order at Finite Temperature Using Entanglement Negativity
• Feasibility of self-correcting quantum memory and thermal stability of topological order
• Geometry and the Hidden Order of Luttinger Liquids: the Universality of Squeezed Space
• Gauging the Kitaev chain
• Channeling quantum criticality
• Entanglement Rényi $\alpha$-entropy
• Physical Implementation of a Majorana Fermion Surface Code for Fault-Tolerant Quantum Computation
• Full Commuting Projector Hamiltonians of Interacting Symmetry-Protected Topological Phases of Fermions
• Characterizing Long-Range Entanglement in a Mixed State Through an Emergent Order on the Entangling Surface
• Hidden order and flux attachment in symmetry protected topological phases: a Laughlin-like approach
• Non-local order parameters for states with topological electromagnetic response

Cited by in corpus (41)

• Non-Abelian Topological Order and Anyons on a Trapped-Ion Processor
• Efficient Long-Range Entanglement using Dynamic Circuits
• Strong-to-Weak Spontaneous Symmetry Breaking in Mixed Quantum States
• Intrinsic Mixed-state Topological Order
• Probing post-measurement entanglement without post-selection
• Separability transitions in topological states induced by local decoherence
• Stability of mixed-state quantum phases via finite Markov length
• Symmetry-enforced many-body separability transitions
• Realizing the Nishimori transition across the error threshold for constant-depth quantum circuits
• Surface codes, quantum circuits, and entanglement phases
• Strong-to-weak symmetry breaking states in stochastic dephasing stabilizer circuits
• Measurement-induced phase transitions in the toric code
• Quantum criticality under imperfect teleportation
• Fractonic Higher-Order Topological Phases in Open Quantum Systems
• Classifying One-Dimensional Quantum States Prepared by a Single Round of Measurements
• Locally Purified Density Operators for Symmetry-Protected Topological Phases in Mixed States
• Stable Symmetry-Protected Topological Phases in Systems with Heralded Noise
• Disentangling transitions in topological order induced by boundary decoherence
• Spontaneous symmetry breaking in open quantum systems: strong, weak, and strong-to-weak
• Gapless Symmetry-Protected Topological States in Measurement-Only Circuits
• Universal Stochastic Equations of Monitored Quantum Dynamics
• An analog of topological entanglement entropy for mixed states
• Decoherence and wavefunction deformation of $D_4$ non-Abelian topological order
• Decoherence through Ancilla Anyon Reservoirs
• Boundary transitions from a single round of measurements on gapless quantum states
• Power-law entanglement and Hilbert space fragmentation in non-reciprocal quantum circuits
• Gauge theory and mixed state criticality
• Preparing matrix product states via fusion: constraints and extensions
• Hierarchy of emergent cluster states by measurement from symmetry-protected-topological states with large symmetry to subsystem cat state
• Mixed-State Topological Order under Coherent Noise
• Quantum Strong-to-Weak Spontaneous Symmetry Breaking in Decohered One Dimensional Critical States
• Subsystem Complexity and Measurements in Holography
• Non-onsite symmetry breaking: topological phase coexistence and criticality
• Measurement and feedforward induced entanglement negativity transition
• Symmetry and Topology of Monitored Quantum Dynamics
• Entanglement and private information in many-body thermal states
• Noisy Monitored Quantum Circuits
• Spacetime Markov length: a diagnostic for fault tolerance via mixed-state phases
• Robust Mixed-State Cluster States and Spurious Topological Entanglement Negativity
• Holographic duality between bulk topological order and boundary mixed-state order
• Entanglement transition in a cluster spin chain coupled with free spins