{"paper":{"title":"Constant-Depth Unitary Preparation of Dicke States","arxiv_id":"2601.10693","primary_cat":"quant-ph","submitted_at":"2026-01-15T18:51:09+00:00","version_compiled":"v3"},"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 v3","sentences":[{"i":0,"p":1.0,"id":"s0","own":false,"role":"background","text":"Dicke states serve as a critical resource in quantum metrology, communication, and computation.","hedge":{"p":1.0,"label":"asserted"},"own_p":0.04,"main_claim_p":0.02,"quantitative":false,"quantitative_p":0.03,"role_probabilities":{"gap":0.0,"method":0.0,"result":0.0,"background":1.0,"limitation":0.0,"future_work":0.0,"contribution":0.0,"interpretation":0.0}},{"i":1,"p":0.86,"id":"s1","own":false,"role":"gap","text":"However, unitary preparation of Dicke states is limited to logarithmic depth in standard circuit models and existing constant-depth protocols require measurement and feed-forward.","hedge":{"p":1.0,"label":"asserted"},"own_p":0.05,"main_claim_p":0.03,"quantitative":true,"quantitative_p":0.94,"role_probabilities":{"gap":0.86,"method":0.0,"result":0.0,"background":0.13,"limitation":0.01,"future_work":0.0,"contribution":0.0,"interpretation":0.0}},{"i":2,"p":1.0,"id":"s2","own":true,"role":"contribution","text":"In this work, we present the first unitary, constant-depth protocols for exact Dicke state preparation.","hedge":{"p":1.0,"label":"asserted"},"own_p":0.96,"main_claim_p":0.84,"quantitative":false,"quantitative_p":0.37,"role_probabilities":{"gap":0.0,"method":0.0,"result":0.0,"background":0.0,"limitation":0.0,"future_work":0.0,"contribution":1.0,"interpretation":0.0}},{"i":3,"p":0.86,"id":"s3","own":true,"role":"method","text":"We overcome the logarithmic-depth barrier by moving beyond the standard circuit model and leveraging global interactions (native to architectures such as neutral atoms and trapped ions).","hedge":{"p":1.0,"label":"asserted"},"own_p":0.78,"main_claim_p":0.14,"quantitative":true,"quantitative_p":0.68,"role_probabilities":{"gap":0.0,"method":0.86,"result":0.0,"background":0.0,"limitation":0.0,"future_work":0.0,"contribution":0.14,"interpretation":0.0}},{"i":4,"p":0.47,"id":"s4","own":true,"role":"contribution","text":"Specifically, utilizing unbounded CZ gates (i.e. within the QAC$^0$ circuit class), we offer circuits for exact computation of constant-weight Dicke states, using polynomial ancillae, and approximation of weight-1 Dicke states (i.e. $W$ states), using only constant ancillae.","hedge":{"p":1.0,"label":"asserted"},"own_p":0.93,"main_claim_p":0.18,"quantitative":true,"quantitative_p":0.84,"role_probabilities":{"gap":0.0,"method":0.43,"result":0.1,"background":0.0,"limitation":0.0,"future_work":0.0,"contribution":0.47,"interpretation":0.0}},{"i":5,"p":0.7,"id":"s5","own":true,"role":"contribution","text":"Granted additional access to the quantum FAN-OUT operation (i.e. upgrading to the QAC$_f^0$ circuit class), we also achieve exact and clean preparation of arbitrary-weight Dicke states, with polynomial ancillae.","hedge":{"p":0.99,"label":"asserted"},"own_p":0.94,"main_claim_p":0.18,"quantitative":true,"quantitative_p":0.68,"role_probabilities":{"gap":0.0,"method":0.03,"result":0.27,"background":0.0,"limitation":0.0,"future_work":0.0,"contribution":0.7,"interpretation":0.0}},{"i":6,"p":1.0,"id":"s6","own":true,"role":"interpretation","text":"These protocols distinguish the constant-depth capabilities of quantum architectures based on connectivity and offer a novel path toward resolving a long-standing quantum complexity 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