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arXiv:2609.17704

Advances in the quantum-state texture theory

Jose Alfredo de Leon, Miguel Gonzalez, Alejandro Fonseca, Pedro C. Azado, Fernando Parisio

quant-phSubmitted Sep 15, 2026• Announced Sep 17, 2026• 0 citations
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Abstract

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.

Comments
29 pages; 22+5 pages excluding references; 2 figures

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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.
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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.