Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:2604.07257 · Journal of Physics A Mathematical and Theoretical

Quantifying and detecting quantum-state texture

Xiangyu Chen, Qiang Lei

quant-phSubmitted Apr 8, 2026• Announced Apr 9, 2026• 2 citations
v1 · Apr 8, 2026v2 · Jun 12, 2026
arXivHTMLPDF

Abstract

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 $\mathcal{T}^{\text{GR}}_{α,z}(ρ)$ based on the $α$-$z$ 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.

Journal reference
Journal of Physics A: Mathematical and Theoretical 2026
DOI
10.1088/1751-8121/ae7b8d

Related papers

Quanutm-State Texture as a Resource: Measures and Nonclassical Interdependencies

Yuntao Cui, Zhaobing Fan, Sun Ho Kim

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.

arXiv:2508.07481•Aug 10, 2025•0 citations

Generalized measures of quantum-state texture via relative entropies and their applications

Wei-Ming Cao, Zhi‐Xiang Jin, Weiming Chen +2 more

Abstract Quantum-state texture (QST) has recently emerged as a novel quantum resource, attracting growing research interest. In this work, we propose several measures to quantify QST using different relative entropies, including the quantum Jensen-Shannon divergence, the sandwiched Rényi relative entropy, and the unified ( α , β ) -relative entropy. We establish that these measures generalize existing fidelity-based measures. Through concrete examples, we demonstrate their advantages over previous approaches, particularly in distinguishing equilibrium states. We further examine quantum channels in the QST framework, showing that many conventional channels are incompatible with this resource theory. Finally, we propose a new class of channels suitable for QST manipulation.

Journal of Physics A Mathematical and Theoretical•Jan 20, 2026•3 citations

Advances in the quantum-state texture theory

Jose Alfredo de Leon, Miguel Gonzalez, Alejandro Fonseca +2 more

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.

quant-pharXiv:2609.17704•Sep 17, 2026•0 citations

Quantum-state block texture and its quantification

Yanjun Chu, Yuhang Xie, Chenyang Cui +1 more

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 $5\times 10^4, 10^5, 5\times 10^5$ 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.

quant-pharXiv:2607.20311•Advanced Quantum Technologies•Jul 23, 2026•0 citations

Quantifying quantum-state texture

Yiding Wang, Hui Liu, Tinggui Zhang

Quantum-state texture is a newly recognized quantum resource that has garnered attention with the advancement of quantum theory. In this work, we introduce several potential quantum-state texture measure schemes and check whether they satisfy the three fundamental conditions required for a valid quantum-state texture measure. Specifically, the measure induced by the ${l}_{1}$ norm serves as a vital tool for quantifying coherence, but we prove that it cannot be used to quantify quantum-state texture. Furthermore, we show that while relative entropy and robustness meet three fundamental conditions, they are not optimal for quantifying quantum-state texture. Fortunately, we still find that there are several measures that can be used as the measure standard of quantum-state texture. Among them, the trace distance measure and the geometric measure are two good measurement schemes. In addition, the two measures based on Uhlmann's fidelity are experimentally friendly and can serve as an ideal definition of quantum-state texture measures in nonequilibrium situations. All this research on quantum-state texture measure theory can enrich the resource theory framework of quantum-state texture.

arXiv:2504.18166•Physical Review A•Apr 23, 2025•13 citations

Quantum-state texture measure and texture transformation

Yufan Lin, Yu Guo, Fei He +1 more

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.

quant-pharXiv:2609.08163•Sep 9, 2026•0 citations
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.
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.
Abstract Quantum-state texture (QST) has recently emerged as a novel quantum resource, attracting growing research interest. In this work, we propose several measures to quantify QST using different relative entropies, including the quantum Jensen-Shannon divergence, the sandwiched Rényi relative entropy, and the unified ( α , β ) -relative entropy. We establish that these measures generalize existing fidelity-based measures. Through concrete examples, we demonstrate their advantages over previous approaches, particularly in distinguishing equilibrium states. We further examine quantum channels in the QST framework, showing that many conventional channels are incompatible with this resource theory. Finally, we propose a new class of channels suitable for QST manipulation.
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.
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.
Quantum-state texture is a newly recognized quantum resource that has garnered attention with the advancement of quantum theory. In this work, we introduce several potential quantum-state texture measure schemes and check whether they satisfy the three fundamental conditions required for a valid quantum-state texture measure. Specifically, the measure induced by the l1{l}_{1}l1​ norm serves as a vital tool for quantifying coherence, but we prove that it cannot be used to quantify quantum-state texture. Furthermore, we show that while relative entropy and robustness meet three fundamental conditions, they are not optimal for quantifying quantum-state texture. Fortunately, we still find that there are several measures that can be used as the measure standard of quantum-state texture. Among them, the trace distance measure and the geometric measure are two good measurement schemes. In addition, the two measures based on Uhlmann's fidelity are experimentally friendly and can serve as an ideal definition of quantum-state texture measures in nonequilibrium situations. All this research on quantum-state texture measure theory can enrich the resource theory framework of quantum-state texture.
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.