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Expansion of Reachable Sets by Zero-Operation Bases

Tatsuki Hirose

Published Jul 8, 2026• 0 citations
Publisher

Abstract

Author's Note (August 24, 2026): This exploratory preprint is currently undergoing methodological re-evaluation. The “zero-operation” bases used to define and expand the reachable sets in this study are being reassessed, including whether these transformations constitute a distinct operator class or are better situated within a broader class of transformations on probability distributions. In particular, I am re-auditing which features of the reported reachable-set expansion are specific to the proposed zero-operation bases and which may instead follow more generally from the choice and enlargement of the available transformation set. The numerical results, their dependence on the chosen operation basis, and the generality of their interpretation are therefore under review. Any necessary corrections, reclassification of claims, or revisions will be documented transparently in a subsequent version. This exploratory preprint analyzes how reachable regions in a four-state probability-distribution space depend on the available zero-operation rule basis. Starting from a Bell-type distribution, it compares symmetric and asymmetric operation bases, showing that mixed rules expand one-dimensional trajectories into higher-dimensional reachable regions, while symmetry constraints can prevent exact reachability of asymmetric targets. This is the fifth manuscript in a preprint series on zero-operation-based quantum computer theory.

DOI
10.5281/zenodo.21265716

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Author's Note (August 24, 2026): This exploratory preprint is currently being re-evaluated as part of a broader methodological audit of the subsequent research program. In particular, the structural interpretation of the reported results and its relationship to later abstract transformation models are being reassessed. This notice does not indicate that the numerical results reported in this preprint have been shown to be incorrect; rather, their interpretation and scope are under review. Any necessary corrections or revisions will be documented transparently in a subsequent version. This exploratory preprint examines whether representative quantum noise channels can be interpreted as distinct modes of structural reconfiguration in observable quantum correlation distributions. Using Bell-state-based simulations, the study compares depolarizing noise, phase damping, and amplitude damping across Z, X, and Y measurement bases. The results suggest that noise-channel type and measurement basis jointly determine whether the observed distribution tends toward preservation, uniformization, fixation, or observation-dependent deformation.