Constructive sources and readers
Quantum Source Completions and Memory–Environment Tradeoffs
Exact source constructions separate reusable quantum memory from environment and retained-history costs.
Jeremy Rodgers · Independent Researcher · 2026-10-27
The question and the results
How much reusable memory does a source need to reproduce a complete stationary output process, and what changes when its environment and archive are also counted?
- For the delayed trine law, the classical HMM minimum is nine states throughout the non-iid range. Quantum memory has minimum dimension four on a proved low-noise interval and three on a certified high-noise interval; the intermediate boundary remains between three and four.
- In the admitted high-noise regime, the exact one-step memory/environment Pareto points are (3, 9) and (4, 3). Minimizing reusable memory and minimizing the recorded-channel environment are different tasks.
- Explicit quantum implementations can share the full passive output law while an additional common intervention distinguishes them. Even an optimum resource count need not identify a unique generator.
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
- 02Question, contributions and operational scope
- 03Stationary quantum completions and the readout interface
- 04A quantitative positive-noise interval requiring four quantum dimensions
- 05A continuous family of minimum-Kraus qutrit sources
- 06The exact memory boundary remains partially open
- 07A four-dimensional source attaining the recorded-channel floor
- 08Universal qutrit lower bounds
- 09A mixed-support qutrit source with lower complete-history cost
- 10A certified non-Weyl source with the same passive law
- 11Access-dependent distinctions at a common resource optimum
- 12Reproducibility and claim status
- 13A universal one-step qutrit dilation bound
- 14References
Technical companion
Technical Companion: Approximation and Accounting for Quantum Sources
Approximation, alternate encodings, output-specific bath costs and causal resource accounting.
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.