Petz map recovery for long-range entangled quantum many-body states
arXiv:2408.00857 · doi:10.1103/PhysRevB.110.195107
Abstract
Given a tripartite quantum state on and the erasure channel on , the rotated Petz map is a recovery channel that acts on to recover the erased quantum information. The infidelity of the best recovery is upper-bounded by the conditional mutual information (CMI). In this work, we study the infidelity of the rotated Petz map on several physically-relevant long-range entangled quantum states. Specifically, we study three classes of quantum phases: (i) steady states of measurement-induced phase transitions, (ii) critical ground state under local measurements, and (iii) chiral states under local measurements. We find that the averaged infidelity of the Petz map recovery sharply distinguishes the three classes: (i) and (ii) are distinguished by the scaling of the infidelity with CMI and (iii) is characterized by an asymmetry of the infidelity with the rotation parameter. We also study Petz map recovery for topological order and find an operational interpretation of the topological entanglement entropy. Our result indicates that recovery fidelity of the Petz map is a useful diagnostic of quantum phases of matter.
Journal version, 9+8 pages, 8+1 figures
References in corpus (38)
- A computable measure of entanglement
- Entanglement Entropy and Quantum Field Theory
- Entanglement in quantum critical phenomena
- Topological entanglement entropy
- Detecting topological order in a ground state wave function
- Zoo of quantum-topological phases of matter
- Local unitary transformation, long-range quantum entanglement, wave function renormalization, and topological order
- Measurement-Induced Phase Transitions in the Dynamics of Entanglement
- Quantum Zeno Effect and the Many-body Entanglement Transition
- Measurement-driven entanglement transition in hybrid quantum circuits
- Theory of the phase transition in random unitary circuits with measurements
- Measurement-induced criticality in random quantum circuits
- Quantum Error Correction in Scrambling Dynamics and Measurement-Induced Phase Transition
- General Relationship Between the Entanglement Spectrum and the Edge State Spectrum of Topological Quantum States
- Critical properties of the measurement-induced transition in random quantum circuits
- Entanglement in a fermion chain under continuous monitoring
- Conformal invariance and quantum non-locality in critical hybrid circuits
- Entanglement and charge-sharpening transitions in U(1) symmetric monitored quantum circuits
- Derivation of holographic negativity in AdS/CFT
- Recoverability in quantum information theory
- Critical and noncritical long range entanglement in the Klein-Gordon field
- Universal recovery maps and approximate sufficiency of quantum relative entropy
- Negativity as the Entanglement Measure to Probe the Kondo Regime in the Spin-Chain Kondo Model
- Entanglement Negativity at Measurement-Induced Criticality
- On Combinatorial Expansions of Conformal Blocks
- Spurious topological entanglement entropy from subsystem symmetries
- Entanglement Domain Walls in Monitored Quantum Circuits and the Directed Polymer in a Random Environment
- Universal tripartite entanglement in one-dimensional many-body systems
- Modular commutator in gapped quantum many-body systems
- Nonlocality and entanglement in measured critical quantum Ising chains
- Multipartitioning topological phases by vertex states and quantum entanglement
- From entanglement generated dynamics to the gravitational anomaly and chiral central charge
- A universal tripartite entanglement signature of ungappable edge states
- Modular Commutators in Conformal Field Theory
- Universal lower bound on topological entanglement entropy
- Approximate reversal of quantum Gaussian dynamics
- Multipartite entanglement in two-dimensional chiral topological liquids
- Recovery Map for Fermionic Gaussian Channels