Constructive sources and readers
Feedback and Robust Local Readout of a Fixed Four-State Quantum Source
Exact and certified reader frontiers identify when feedback improves access to a fixed source target.
Jeremy Rodgers · Independent Researcher · 2026-10-27
The question and the results
When does choosing a measurement from earlier retained records improve a local reader’s ability to decide the sign of a fixed four-state source?
- Adaptive and randomized nonadaptive continuous equatorial readers have equal minimax risk through three copies for every shared efficiency and visibility. At four copies, rational policies and continuous lower certificates prove strict feedback advantages in the ideal and specified noisy models.
- For the nominal one-percent task, the copy minimum is in [13, 14] for both classes. Under the original asymmetric fixed calibration uncertainty, both minima are in [16, 17]. These intervals do not establish a one-percent feedback separation.
- Finite policy graphs, exact risk evaluation and explicit controller/archive accounts separate copy savings from total apparatus savings. The hidden label stays fixed across each complete conditional-copy experiment.
Connections to the programme
The complete argument.
Read every section on site, including the mathematics, proofs, examples and references. Each section has its own address for citation and navigation.
- 01Orientation and abstract
- 02Task, contributions and operational contract
- 03Continuous equatorial access: exact small-horizon optima and an improved fixed reader
- 04Continuous equatorial readers: exact equality through three copies
- 05Certified continuous nonadaptive obstructions
- 06A robust frozen reader without X/Y symmetry
- 07Robust readers: a convex-hull theorem and a global copy lower bound
- 08Local-effect certificates for larger copy budgets
- 09Frozen-angle randomization and preparation convexification
- 10Compact, exactly certified adaptive readers at thirteen and fourteen copies
- 11Physical resources and remaining boundaries
- 12Adaptive phase readers: exact scope, optimum and genuine feedback gain
- 13One reader across unknown erasure and calibration parameters
- 14Reproducibility and assistance disclosure
- 15References
Technical companion
Technical Companion: Reader Methods and Resource Interfaces
Weighted readout design, continuous reader bounds, calibration and explicit resource certificates.
Read the complete companion →Publication and computational material.
Original PDFComplete searchable textOriginal verification supplement ZIPReading inventoryThe supplied publication is a PDF. Prose reflows as HTML where its notation permits; complex mathematical passages retain their exact source-vector layout with searchable transcriptions. The transcription preserves extracted symbols rather than fraction or matrix structure.