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Reexamining the role of state texture in gate identification and fixed-point resource theories

Alexander C. B. Greenwood1,*, Joseph M. Lukens2,3, Li Qian1, and Brian T. Kirby4,5

  • *Contact author: alexander.greenwood@mail.utoronto.ca
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Phys. Rev. A 114, 032411 – Published 4 September, 2026

DOI: https://doi.org/10.1103/83pf-837s

Abstract

A protocol for identifying controlled-not (cnot) gates versus single-qubit-only gates in universal quantum circuits using randomized input states was recently shown to be intimately connected to the quantum resource of state texture. Here, we revisit this gate identification protocol and demonstrate that a more general fidelity-based formulation succeeds for nearly all laboratory bases. We then examine a broader family of quantum resource theories, where a distinct resource theory can be defined for each choice of reference pure state, establishing core resource-theoretic requirements without the computational shortcut offered by the “grand sum” employed in the original formulation of state texture. By extending from single “resourceless” states to convex sets via a convex-roof construction, we recover single-qubit measures of known resource theories such as imaginarity and coherence. Finally, we introduce a family of “fixed-point resource theories” that includes fixed-point instances of the theories of state texture, genuine coherence, purity, and athermality. For these fixed-point resource theories we show that under free operations the fidelity-based lower bound is weakly monotonic, while specific violations of strong monotonicity are found for the convex-roof logarithmic measure.

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Phys. Rev. A 114, 032411– Published 4 September, 2026
  • Received 12 March 2026
  • Accepted 10 July 2026
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

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