Quantum Source Completions and Memory–Environment Tradeoffs
Orientation and abstract
Quantum Source Completions and Memory–Environment Tradeoffs
Jeremy Rodgers Independent Researcher www.everythingequation.com
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27 October 2026
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https://doi.org/10.5281/zenodo.23721088
Abstract
We quantify stationary quantum-source resources under explicit readout and retained-output contracts. Orthogonal-current-symbol completions of stationary triple data have exact minimum dimension equal to the sum of their complex positive-semidefinite slice ranks. For delayed phase-circle processes we give a dimension-four emitted-symbol realization and prove noiseless optimality. The delayed trine specialization has classical HMM minimum nine for every non-iid parameter, quantum minimum four at sufficiently low noise and three on a certified high-noise interval. A continuous qutrit family attains one-step recorded-channel Choi rank nine, while a four-dimensional latitude source attains three, giving an exact two-point Pareto frontier on that interval. At noise
mixed-support qutrit source lowers complete-history Choi rank to 50, 152 and 456 3
at horizons two, three and
4; universal lower bounds are 48, 145 and 437 3
. Full-word proofs, algebraic CP certificates and output-specific optima separate internal memory from retained-history dilation cost. The exact intermediate memory boundary and full-history optimum remain open. These are operational quantum-source results under standard probabilities, not ontology or total-hardware theorems.