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Journal of Physics A Mathematical and Theoretical

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

Wei-Ming Cao, Zhi‐Xiang Jin, Weiming Chen, Yan-Ling Wang, Bing Yu

Published Jan 20, 2026• 3 citations
Publisher

Abstract

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.

DOI
10.1088/1751-8121/ae3aea

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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.
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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 speed limits impose intrinsic lower bounds on the shortest time scale for quantum system evolution. As an emerging paradigm in quantum resource theory, quantum-state texture has attracted research interest amid the rapid advancement of quantum theory. Herein, we investigate the interplay between quantum speed limits and quantum-state texture via several canonical quantifiers, including trace distance, state rugosity and Jensen-Shannon divergence. To demonstrate our findings, we analyze the minimum evolution time of physical systems subject to dephasing and dissipative dynamics. For the Jensen-Shannon divergence, we further explore nonunitary dynamics described by completely positive and trace-preserving maps, taking the amplitude damping channel as a typical example. In addition, we explore the tightness of these bounds in the considered dynamical models. Our results reveal that quantum speed limits derived from quantum-state texture capture the fundamental constraints on quantum evolutionary speed, with promising applications in quantum computing, quantum control and quantum metrology.
Quantum-state texture (QST) has found applications in several fields from quantum foundations and computation to quantum criticality. However, a general theory of QST dynamics under arbitrary physical processes remains unavailable, limiting both its practical application and experimental exploration. Here, we demonstrate that the QST response to an arbitrary finite-dimensional channel is fully encoded in the dual evolution of a single reference state. This description yields necessary and sufficient conditions for texture preservation and implies exact conservation under all free-unital dynamics. Using a nuclear magnetic resonance quantum processor, we experimentally verify these predictions across distinct channel classes. Furthermore, we show that local QST measurements provide an operational signature of entangling gates in circuit layers. Our results establish quantum-state texture as a resource and a practical diagnostic tool in quantum information processing.
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.