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Laser Physics Letters

Quantum-state texture of assistance via the trace distance and Bures measures

Wenhua Wang, Zhengli Chen

Published Sep 1, 2026• 0 citations
Publisher

Abstract

Abstract Quantum-state texture has recently been recognized as a legitimate quantum resource, attracting increasing attention alongside the development of quantum theory. In this work, we investigate quantifications of the quantum-state texture of assistance based on the trace distance and Bures measures, which characterize the maximum possible average texture over all pure-state decompositions of a given quantum state. We show that both quantities are bounded and concave, the former is monotonic, whereas the latter is not. Notably, we derive the closed-form expressions for these two quantities. Furthermore, we establish global-versus-marginal bounds for them for any bipartite state. Both quantities satisfy subadditivity, and for product states, the global and partial quantities are each related by an equality.

DOI
10.1088/1612-202x/ae9ea5

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Abstract Quantum-state texture has recently been recognized as a legitimate quantum resource, attracting increasing attention alongside the development of quantum theory. In this work, we investigate quantifications of the quantum-state texture of assistance based on the trace distance and Bures measures, which characterize the maximum possible average texture over all pure-state decompositions of a given quantum state. We show that both quantities are bounded and concave, the former is monotonic, whereas the latter is not. Notably, we derive the closed-form expressions for these two quantities. Furthermore, we establish global-versus-marginal bounds for them for any bipartite state. Both quantities satisfy subadditivity, and for product states, the global and partial quantities are each related by an equality.
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.
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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 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.
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.