Preparation with a retained past
Conditional Gaussian Preparation with Retained Archives
Prepare a Gaussian writer while retaining its archives, with an explicit conditional readiness bound and a one-use instrument comparison.
Jeremy Rodgers · Independent Researcher · 9 October 2026
9 October 2026 manuscript
The argument
Preparation with every archive still present
A preparation procedure must work with the information the apparatus actually retains. This construction keeps the writer, every preparation archive, and a separate measurement receiver in one complete description. Smooth harmonic controls split the writer, copy its branch into an archive, and return its wave to the ready form. The exact configuration map tracks where the earlier information goes.
The decisive estimate concerns the writer together with its entire actual archive. It bounds their joint law against a ready writer paired with the archive’s unchanged actual marginal. Weak relative-score and moment assumptions on the full original conditional law make this preparation quantitative without a density cap. An explicit bank with 102 positional coordinates achieves readiness below 0.000010052.
The same finite construction then supports one unknown internal input and a distinct physical receiver. Under the stated preparation and holding conditions, the labelled projective-instrument comparison has the same error ceiling for any finite internal reference. The receiver records the earlier writer event and keeps its sign during the specified hold. The arguments below retain the exact maps, inverse, exceptional sets, and complete error calculation.
Follow the physical map
Start with the translated Gaussian packets and their complete guidance current. The resulting smooth map gives the physical realization, preserves reference area, and keeps an explicit inverse.
Read the argument →Keep the whole archive in the estimate
The preparation comparison includes all final archive coordinates and unused sources. Sectional variation controls the error while the archive retains its actual distribution.
Read the argument →See what the statistical assumptions buy
Physical weak scores control variations on a finite box; actual moments pay for its tails. This is the route to the explicit finite bank and its numerical readiness bound.
Read the argument →Use the prepared writer
The instrument construction loads the unknown input after warmup, copies the writer’s event into another coordinate, and controls the labelled output with a finite internal reference.
Read the argument →This paper supplies the portfolio’s conditional-preparation and one-use instrument construction. The repeated-record paper develops a separate reader, copy gate, and reset bank. Connecting the two requires readiness conditional on that entire bank and operations that preserve the prepared writer’s stated interface. The flow and current papers provide further tools for extending the analysis to more general parents.
The complete paper
Follow the full argument.
Every section, proof and appendix, with linked equations and the complete bibliography.
- OpeningAbstract and publication identity
- Section 1The preparation question
Relation to established and prior work
- Section 2Laws, configurations and error metrics
- Section 3A smooth copy–return map on the complete configuration
Finite separation and retained fine information
- Section 4Complete-law preparation with every archive retained
- Section 5Physical relative scores without a density cap
Finite-resource existence and growing conditional prefixes · Two distinct cap-free limits
- Section 6Robustness under complete physical map errors
Full-dimensional concentration from physical scores · A sharper two-coordinate distortion criterion
- Section 7One unknown input and a separate held receiver
The complete current and the generic-input map · Own-outcome copying uniformly in the input · The actual conditional-state metric · The coherent 102-coordinate row
- Section 8Instrument stability, reference systems, and postselection
An abstract full-ready criterion · Cap-free transfer of conditional quantum states · What the cq estimate says after selecting an outcome · Physical scope of the one-use result
- Appendix AA complementary finite regular-basin theorem
- Appendix BPhysical scope and relation to companion work
- OpeningConclusion
- OpeningAuthor statement and research support
- OpeningBibliography