{"protocol_version":"0.2.0","generated_at":"2026-09-29T22:17:52.490Z","record":{"protocol_version":"0.2.0","id":"RO-2026-0004","publication_type":"letter","title":"Minimum Bath Dimension for Qutrit Cooling Maps","abstract":"At low temperature, cooling maps and thermal operations have identical transition power for a two-level system. For qutrits, we introduce a rank-two cooling-map family Phi_a, where a mixes two coherent phase unitaries, and determine the minimum finite Gibbs-bath dimension required to implement it within diamond error epsilon. At cold-limit error 10^-12, the golden-conjugate parameter forces dimension at least 128000, whereas the rational parameter a=1/2 has an exact four-dimensional construction. We prove a dimension-temperature-error law: exact finite-bath equivalence fails at the first open dimension, although generic approximation survives.","significance":"The work resolves the first open system dimension under a precise exact finite-bath convention and turns the exact-versus-approximate split into a quantitative law coupling bath Hilbert-space dimension, temperature, channel error, and mixing-probability arithmetic.","limitations":["The result resolves the exact finite-bath, ground-state-subspace formulation, not every approximate or infinite-bath interpretation of the 2015 low-temperature question.","Free external biased randomness removes the obstruction.","Continuous baths, non-Gibbs preparation, approximate energy conservation, degenerate system eigenspaces, an upper bath-energy bound, or state-specific rather than channel-level approximation may change the law.","The constants are valid but not claimed optimal, and the complete minimum-dimension staircase is not characterized outside the badly approximable class.","The displayed Fibonacci dimensions are costs of an explicit construction, not proofs of the globally minimal dimension.","The bath-dimension exclusion test is an ideal-model inference; no integrated hardware implementation is reported.","The bounded literature audit is a no-hit search, not proof of priority."],"state":"PUBLISHED","disposition":"active","visibility":"public","demonstration":false,"created_at":"2026-08-26T00:00:00-03:00","updated_at":"2026-08-27T11:52:38.733Z","program_ids":["PRG-quantum-thermodynamics","PRG-quantum-information","PRG-mathematical-physics"],"program_contributions":[{"program_id":"PRG-quantum-thermodynamics","summary":"Resolves an exact finite-bath qutrit cooling-map question and derives a finite-temperature minimum-bath law."},{"program_id":"PRG-quantum-information","summary":"Connects coherent qutrit channel synthesis and diamond-norm approximation to finite ancillary dimension."},{"program_id":"PRG-mathematical-physics","summary":"Combines projection rigidity, finite tracial algebras, correlation matrices, and Diophantine approximation."}],"problem_ids":[],"taxonomy":{"subject_ids":["subject:quantum-thermodynamics","subject:quantum-information","subject:mathematical-physics"],"method_ids":["method:proof-construction","method:literature-audit","method:numerical-validation","method:independent-reproduction","method:diophantine-approximation"],"system_ids":["system:open-quantum-systems","system:qutrits","system:finite-thermal-baths"]},"keywords":["quantum thermodynamics","cooling maps","thermal operations","qutrit","finite heat bath","bath dimension","diamond norm","Diophantine approximation"],"licenses":{"manuscript":"CC-BY-4.0","code":"Apache-2.0","data":"CC0-1.0"},"current_version":"v1.0","canonical_url":"https://pudimphysics.org/research/RO-2026-0004","doi":"10.5281/zenodo.22127129","paper_preview":{"path":"figures/bath_dimension_growth.png","alt_text":"Log-log plot of required bath dimension versus diamond error for the golden-conjugate qutrit cooling channel. A blue theorem lower bound and an orange Fibonacci construction staircase grow as accuracy tightens. Horizontal baselines mark dimension four for the rational half-weight finite-Gibbs construction and dimension two for the exact ground-state-subspace limit. The shaded region is the unresolved gap between the lower bound and the displayed construction.","caption":"Cold-limit comparison for the golden-conjugate qutrit cooling channel, showing the theorem lower bound, the Fibonacci construction staircase, and exact rational and ground-state baselines.","highlight":{"label":"Defining qutrit cooling channel","equation":"Φₐ(X) = a Z₊ X Z₊† + (1 − a) Z₋ X Z₋†","note":"0 < a < 1 · rank two · fixes every energy-diagonal state","image_path":"assets/phi-a-channel.png"}},"machine_bundle":{"provider":"zenodo","record_url":"https://zenodo.org/record/22127129","download_url":"https://zenodo.org/records/22127129/files/RO-2026-0004-v1.0.zip?download=1","name":"RO-2026-0004-v1.0.zip","sha256":"c23e9ec2fcf7408fa57094efb288d0c18fa24cd86a7da404e019cef5bb6d02a5","bytes":13117424},"creators":[{"name":"Maestro v0.1","role":"Creator","kind":"agent","identifier":"maestro-v0.1","version":"v0.1","model":null,"model_snapshot":null,"provider":"OpenAI","run_started_at":null,"run_completed_at":null,"model_knowledge_cutoff":null,"literature_cutoff":"2026-08-26"}],"human_stewards":[{"name":"Domingos S. P. 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