Quantum-state texture measure and texture transformation

Abstract

Quantum-state texture quantifies structural irregularities of a state in a selected basis and has emerged as a valuable resource for gate characterization in universal circuits. Consequently, a class of contractive distance based texture measures and a framework for constructing convex-roof extended texture measure have been proposed. Here, we extend this theory in several directions. We examine the convertibility of a pure state to any state under texture-free operations, and fully solve the deterministic transformation problem between any two states in the qubit case. We then propose two classes of texture measures: convex-function-based measures and texture cost defined via minimal cost of texture contained in pure states. Moreover, we show that every texture monotone gives rise to a non-negative function which admits the same properties as the function used in the convex-roof extension---thus providing a converse to that construction. Our work thereby offers a relatively comprehensive resource-theoretic formulation of quantum-state texture.

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BibTeX RIS

BibTeX

@misc{lin2026quantumstate,
  title = {{Quantum-state texture measure and texture transformation}},
  author = {Yufan Lin and Yu Guo and Fei He and Shuanping Du},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.08163},
  eprint = {2609.08163},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.08163},
  note = {CC BY-NC-ND 4.0},
}

RIS

TY  - UNPB
TI  - Quantum-state texture measure and texture transformation
AU  - Yufan Lin
AU  - Yu Guo
AU  - Fei He
AU  - Shuanping Du
PY  - 2026
DA  - 2026/09/08
PB  - arXiv
DO  - 10.48550/arxiv.2609.08163
UR  - https://arxiv.org/abs/2609.08163
AB  - Quantum-state texture quantifies structural irregularities of a state in a selected basis and has emerged as a valuable resource for gate characterization in universal circuits. Consequently, a class of contractive distance based texture measures and a framework for constructing convex-roof extended texture measure have been proposed. Here, we extend this theory in several directions. We examine the convertibility of a pure state to any state under texture-free operations, and fully solve the deterministic transformation problem between any two states in the qubit case. We then propose two classes of texture measures: convex-function-based measures and texture cost defined via minimal cost of texture contained in pure states. Moreover, we show that every texture monotone gives rise to a non-negative function which admits the same properties as the function used in the convex-roof extension---thus providing a converse to that construction. Our work thereby offers a relatively comprehensive resource-theoretic formulation of quantum-state texture.
ER  -

Abstract

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