Sharp universal death of entanglement threshold for Pauli Hamiltonians

arXiv:2609.30149 · quant-ph, math-ph, math.MP · Submitted 2026-09-24 · Read on arXiv

quant-ph, math-ph, math.MP

Submitted: 2026-09-24

Updated: 2026-09-24

Terminology

• Gibbs State — 27× in this paper · explained in 2 episodes
• Entanglement — 15× in this paper · explained in 4 episodes
• Cluster expansion — 9× in this paper · explained in 2 episodes
• Trace — 8× in this paper · explained in 2 episodes
• Approximate Counting — 2× in this paper · explained in 1 episode
• Frustration — 2× in this paper · explained in 2 episodes
• Accuracy — 1× in this paper · explained in 1 episode
• Distillation — 1× in this paper · explained in 2 episodes
• Hilbert Space — 1× in this paper · explained in 2 episodes
• Phase Transitions — 1× in this paper · explained in 2 episodes
• Stabilizer States — 1× in this paper · explained in 2 episodes
• Trace Distance — 1× in this paper · explained in 3 episodes

Sources

• High-Temperature Gibbs States are Unentangled and Efficiently Preparable
• The repulsive lattice gas, the independent-set polynomial, and the Lov'asz local lemma
• Correlation decay and partition function zeros: Algorithms and phase transitions
• Contraction: a Unified Perspective of Correlation Decay and Zero-Freeness of 2-Spin Systems
• Location of zeros for the partition function of the Ising model on bounded degree graphs
• Separability Criterion for Density Matrices
• Separability of Mixed States: Necessary and Sufficient Conditions
• When quantum thermal states look classical
• Efficient Algorithms for Approximating Quantum Partition Functions
• High-temperature cluster expansion for classical and quantum spin lattice systems with multi-body interactions
• Bounds on the Complex Zeros of (Di)Chromatic Polynomials and Potts-Model Partition Functions
• The Enumeration of Vertex Induced Subgraphs with respect to the Number of Components
• Stabilizer Codes and Quantum Error Correction
• Arboreal Bound Entanglement
• Classical algorithms, correlation decay, and complex zeros of partition functions of quantum many-body systems
• Deterministic polynomial-time approximation algorithms for partition functions and graph polynomials
• Algorithmic Pirogov-Sinai theory
• Polynomial-Time Approximation of Zero-Free Partition Functions
• Algorithmic Cluster Expansions for Quantum Problems
• Convergence of the Cumulant Expansion and Polynomial-Time Algorithm for Weakly Interacting Fermions

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