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.

arXiv:2609.08163 [quant-ph]

(or arXiv:2609.08163v1 [quant-ph] for this version)

https://doi.org/10.48550/arXiv.2609.08163 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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