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arXiv:2609.08163

Quantum-state texture measure and texture transformation

Yufan Lin, Yu Guo, Fei He, Shuanping Du

quant-phSubmitted Sep 8, 2026• Announced Sep 9, 2026• 0 citations
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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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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.
Quantum-state texture is a newly recognized quantum resource that has garnered attention with the advancement of quantum theory. In this work, we address several key aspects of quantum-state texture resource theory, including the quantification of quantum-state texture, quantum state transformation under free operations, and the relationships between quantum resources. We first propose two new measures of quantum-state texture and introduce a specific functional form for constructing such measures via the convex roof method. Then, we determine the maximum probability of quantum state transformation under free operations. Finally, we establish connections between quantum-state texture and other prominent quantum resources, such as coherence, imaginarity, and predictability. Our research contributes to the measure theory of quantum-state texture and enriches the overall framework of quantum-state texture resource theory.
The recently introduced concept of quantum-state texture (QST) has found applications ranging from the identification of unknown quantum gates to the study of quantum phase transitions and criticality, and has already been experimentally investigated. Here, we advance its resource-theoretic formulation in several directions. Our approach centers on the experimentally accessible grand sum--the sum of all matrix elements of a density operator in a given basis. We clarify several points raised in the recent literature, including the relation between texture distillation and a simple grand-sum-based QST monotone. We completely characterize free operations for a single qubit and study the resulting state-conversion order; classify relevant families of free operations in arbitrary dimensions; derive bounds relating the texture of composite systems to that of their subsystems; and introduce the basis-independent concept of set texture. Together, these results strengthen and broaden the resource theory of QST, providing a foundation for its further development and applications.
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Quantum-state texture (QST) is an emerging quantum resource that has garnered increasing attention amid advances in quantum theory. In this work, we generalize the QST to quantum-state block texture (QSBT). This generalization provides profound operational interpretations for quantifying the advantages of quantum states in quantum information processing. We pioneer an alternative framework for characterizing and quantifying quantum-state block texture, and propose three types of block texture measures. By comparing these QSBT measures, we investigate their distinctions and interrelationships. We demonstrate that the geometric measure serves as an upper bound for the trace distance-based measure. For a specific family of quantum states, we evaluate the values of two trace distance-based measures. Then we sample four sets of data from this family of states, with each set comprising 5×104,105,5×1055\times 10^4, 10^5, 5\times 10^55×104,105,5×105 and $10^6 $ samples, respectively, and present the corresponding distributions. Our results reveal that the QSBT measures constructed via different approaches show distinct characteristics, indicating their potential roles in quantifying the block texture of quantum states.
We introduce and explore the notion of texture of an arbitrary quantum state, in a selected basis. In the first part of this Letter we develop a resource theory and show that state texture is adequately described by an easily computable monotone, which is also directly measurable. It is shown that textures are useful in the characterization of unknown quantum gates in universal circuit layers. By using randomized input states and recording the textures of the output qubits we are able to fully characterize the circuit layer, whenever it contains at least one CNOT gate. This can be done without the need of tomographic protocols and the use of ancillary systems.
Quantum-state texture is a recently proposed quantum resource that characterizes the inhomogeneity of a quantum state's matrix element distribution in the computational basis, enriching our understanding of quantum state structure. To expand its quantification toolkit and establish detection methods, in this article, we investigate the resource theory of texture from both quantitative and detection perspectives. First, we construct a texture measure Tα,zGR(ρ)\mathcal{T}^{\text{GR}}_{α,z}(ρ)Tα,zGR​(ρ) based on the ααα-zzz Rényi relative entropy and present some of its inherent properties. Second, we analyze the mathematical relationships between several existing texture measures, revealing connections among different quantifiers. Finally, drawing on the witness concept from other resource theories, we systematically introduce texture witnesses into the texture theory and provide examples of texture witnesses with special properties.