{"paper":{"title":"Entanglement entropy and magic of ZX-diagrams","arxiv_id":"2610.12447","primary_cat":"quant-ph","submitted_at":"2026-10-08T17:58:32+00:00","version_compiled":"v1"},"notice":"Every quoted sentence is the authors' text from the arXiv listing abstract. Labels and probabilities are the outputs of classifier-1.13.0 on the question bank abstract-p1-20260923, exactly as returned. No sentence in this record was written by a language model.","schema":"pith.compiled-record/v0","status":"compiled","abstract":{"source":"arXiv listing abstract v1","sentences":[{"i":0,"p":0.94,"id":"s0","own":false,"role":"background","text":"Entanglement and non-stabilizerness are complementary resources underlying the complexity of quantum states, yet extracting either quantity from large quantum circuits generally requires exponentially scaling resources.","hedge":{"p":0.99,"label":"asserted"},"own_p":0.05,"main_claim_p":0.03,"quantitative":true,"quantitative_p":0.65,"role_probabilities":{"gap":0.06,"method":0.0,"result":0.0,"background":0.94,"limitation":0.0,"future_work":0.0,"contribution":0.0,"interpretation":0.0}},{"i":1,"p":0.95,"id":"s1","own":false,"role":"background","text":"In diagrammatic approaches to quantum computation, such as the ZX-calculus, both quantities likewise typically require expensive tensor contractions that are not native to graphical rewriting.","hedge":{"p":0.93,"label":"asserted"},"own_p":0.05,"main_claim_p":0.02,"quantitative":false,"quantitative_p":0.28,"role_probabilities":{"gap":0.05,"method":0.0,"result":0.0,"background":0.95,"limitation":0.0,"future_work":0.0,"contribution":0.0,"interpretation":0.0}},{"i":2,"p":0.95,"id":"s2","own":true,"role":"contribution","text":"Here we show that both entanglement and magic can be efficiently estimated directly from ZX-diagrams.","hedge":{"p":1.0,"label":"asserted"},"own_p":0.96,"main_claim_p":0.91,"quantitative":false,"quantitative_p":0.1,"role_probabilities":{"gap":0.0,"method":0.0,"result":0.05,"background":0.0,"limitation":0.0,"future_work":0.0,"contribution":0.95,"interpretation":0.0}},{"i":3,"p":0.98,"id":"s3","own":true,"role":"method","text":"Flow enables efficient extraction of a normal form separating a potentially extensively entangled graph-state backbone from non-Clifford Pauli gadgets.","hedge":{"p":0.98,"label":"asserted"},"own_p":0.76,"main_claim_p":0.08,"quantitative":false,"quantitative_p":0.08,"role_probabilities":{"gap":0.0,"method":0.98,"result":0.0,"background":0.0,"limitation":0.0,"future_work":0.0,"contribution":0.02,"interpretation":0.0}},{"i":4,"p":0.51,"id":"s4","own":true,"role":"method","text":"This structure yields additive upper and lower bounds on bipartite entanglement entropy, which we further tighten through a preprocessing procedure that removes or merges redundant non-Clifford contributions.","hedge":{"p":1.0,"label":"asserted"},"own_p":0.93,"main_claim_p":0.1,"quantitative":true,"quantitative_p":0.86,"role_probabilities":{"gap":0.0,"method":0.51,"result":0.42,"background":0.0,"limitation":0.0,"future_work":0.0,"contribution":0.07,"interpretation":0.0}},{"i":5,"p":0.84,"id":"s5","own":true,"role":"result","text":"The same normal form gives an upper bound on logarithmic stabilizer extent.","hedge":{"p":1.0,"label":"asserted"},"own_p":0.9,"main_claim_p":0.09,"quantitative":true,"quantitative_p":0.9,"role_probabilities":{"gap":0.0,"method":0.02,"result":0.84,"background":0.0,"limitation":0.0,"future_work":0.0,"contribution":0.14,"interpretation":0.0}},{"i":6,"p":0.89,"id":"s6","own":true,"role":"result","text":"We benchmark these methods in random unitary and monitored circuits, and a circuit combining Trotterized Hamiltonian evolution with Clifford layers, finding that the resulting bounds remain informative even at large qubit numbers, circuit depths, and internal spider counts.","hedge":{"p":1.0,"label":"asserted"},"own_p":0.97,"main_claim_p":0.12,"quantitative":false,"quantitative_p":0.22,"role_probabilities":{"gap":0.0,"method":0.07,"result":0.89,"background":0.0,"limitation":0.0,"future_work":0.0,"contribution":0.04,"interpretation":0.0}},{"i":7,"p":0.99,"id":"s7","own":true,"role":"interpretation","text":"Our results provide scalable probes of entanglement and non-stabilizerness of ZX-diagrams and establish a bridge between ZX-calculus and quantum many-body resource characterization, with applications across quantum computing, quantum information, and condensed-matter physics.","hedge":{"p":1.0,"label":"asserted"},"own_p":0.82,"main_claim_p":0.63,"quantitative":false,"quantitative_p":0.05,"role_probabilities":{"gap":0.0,"method":0.0,"result":0.0,"background":0.0,"limitation":0.0,"future_work":0.0,"contribution":0.01,"interpretation":0.99}}]},"compiled":{"main_claim":{"p":0.76,"text":"Here we show that both entanglement and magic can be efficiently estimated directly from ZX-diagrams.","location":"abstract s2","hedge_strength":{"p":1.0,"label":"asserted"}},"provenance":{"route":{"via":"TypeSafe API","model":"classifier-1.13.0","endpoint":"https://api.typesafe.ai/v1/systemone","provider":"TypeSafe"},"packing":"one request per 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