Retained Quantum Records: Recovery Limits and Control-Dependent Formation Costs

AbstractRetained measurement records constrain recoverability, but their formation also depends on the available physical controls. We give exact, constructively attained answers to both questions in two specified models. For a balanced nondemolition qubit process with actual binary observer memories unavailable to the decoder, we determine the maximum recovery compatible with average readout accuracy and pair agreement. The finite-record solution includes its feasible region and a common memory-writing and recovery process, without assuming exchangeability of observed records. Under a complete conditional-pairwise-independence promise at fixed informative accuracy, the optimal coherence has a sharp inverse-square-root asymptotic; fully conditionally independent records instead give exponential decay. Thus identical single-record and pair-record calibrations need not justify the product-law recovery bound. We then fix a logical code in four spin-3/2 systems and sequential diagonal contacts with exact controlled-swap endpoints. Hard budgets for net contact action and added spectral control charge yield an exact peak-excursion frontier within a declared quadratic-plus-cubic control class. A single positive-amplitude preparation jointly attains the record, recovery and occupation requirements, connecting the two results through an exact finite-dimensional optimization. A closed three-record example distinguishes fixed complete records from fixed averaged data. Separately calibrated imperfect contacts admit one-sided finite-error extensions. Together, the results characterize both informational compatibility and control-dependent formation through common attaining apparatuses.Preprint status and related materialsPREPRINT - AUTHOR-SUBMITTED MANUSCRIPT; NOT PEER REVIEWED OR ACCEPTED FOR PUBLICATION. This theoretical and computational work addresses the compatibility of retained binary quantum records with optimized accessible-system recovery, and the control-dependent resources required to form those records in a specified spin encoding. The article provides exact finite-record bounds, attainable recovery and resource frontiers, and calibrated finite-error qualifications. The manuscript has been submitted to Foundations of Physics for journal consideration; this Figshare record is not a journal publication. The technical supplement is included as a second PDF in this same record. Related software, verification code, exact certificates, and selected computational evidence are available separately at https://doi.org/10.6084/m9.figshare.34886079 under the MIT licence. When a journal version of record becomes available, a link to its DOI will be added here.AuthorKent Nimmo; Independent Researcher, Vancouver, British Columbia, Canada; ORCID 0009-0003-8503-8891.