{"arxiv_id":"2602.17258","incoming":{"papers":4,"sentences":7,"groups":[{"kind":"method_or_tool","label":"Uses its method or tool","papers":2,"sentences":2,"quotes":[{"arxiv_id":"2608.19325","title":"Statistical Mechanics of Non-Abelian Learnability Transitions","url":"/paper/2608.19325","section":"Introduction","sentence":"Loop model and replica pairings.—Following the stat-mech framework for monitored circuits [ref] , we compute both diagnostics by contracting a replicated tensor network on the circuit spacetime, with $Q$ forward and $Q$ backward replicas.","intent_p":0.96,"contests_p":null},{"arxiv_id":"2604.25640","title":"Continuous Reset-Induced Phase Transition in Measurement-Free Random Quantum Circuits","url":"/paper/2604.25640","section":"EFFECTIVE SPIN MODEL","sentence":"By following [ref] , the replica logarithmic Rényi-$n$ purity for the circuit is given by [equation] where [equation] $ρ$ is a mixed state and $𝔼_u$ represents the average manipulation for the Haar random unitary gates [ref] .","intent_p":0.95,"contests_p":null}]},{"kind":"background","label":"Cites it as background","papers":3,"sentences":3,"quotes":[{"arxiv_id":"2608.19325","title":"Statistical Mechanics of Non-Abelian Learnability Transitions","url":"/paper/2608.19325","section":"Introduction","sentence":"(See Refs. [ref] for reviews.) When the dynamics preserves a global symmetry, the conserved charge becomes a natural target: how quickly the record reads out its value changes parametrically with system size across the charge-sharpening transition [ref] .","intent_p":0.94,"contests_p":null},{"arxiv_id":"2607.08589","title":"Universality of Measurement-Induced Criticality under Symmetry-Breaking Measurements","url":"/paper/2607.08589","section":"Introduction","sentence":"A paradigmatic setting for studying MIPTs is provided by random quantum circuits [ref] .","intent_p":0.94,"contests_p":null},{"arxiv_id":"2605.27350","title":"Postselection-free ballistic-diffusive transition in monitored spin chains","url":"/paper/2605.27350","section":"Introduction","sentence":"The study of monitored quantum systems has experienced a renaissance in recent years, driven by advances on both theoretical and experimental fronts [ref] .","intent_p":0.96,"contests_p":null}]}],"unlabelled_sentences":2},"outgoing":{"papers":3,"sentences":3,"groups":[{"kind":"background","label":"Cites as background","papers":1,"sentences":1,"quotes":[{"arxiv_id":"1803.00089","title":"Coarse-grained dynamics of operator and state entanglement","url":"/paper/1803.00089","section":"Discussion","sentence":"Since the original papers, random quantum circuits have become part of the standard toolbox to study chaotic quantum dynamics, and provided crucial insights into, e.g thermalization and entanglement growth [ref] , many-body quantum chaos [ref] and operator spreading [ref] , or the emergence of irreversible hydrodynamics from unitary evolution [ref] .","intent_p":0.93,"contests_p":null}]}],"unlabelled_sentences":2},"claims":[],"thresholds":{"intent_p":0.8,"supports_p":0.95,"contests_p":0.7},"method":"Citing sentences come from each paper's LaTeX source; every \\cite marks the sentence and the works it cites. Pith's classifier typed each sentence. A label is shown at intent probability 0.8 or more (0.95 for support), a contest at 0.7 or more. Measured accuracy against two blind model families is at https://pith.science/accuracy. The quoted sentences are the citing authors' own.","held_up":null,"_links":{"html":"https://pith.science/paper/2602.17258"}}