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arXiv:2507.13862 · Physical Review A

Role of quantum state texture in probing resource theories and quantum phase transitions

Ayan Patra, Tanoy Kanti Konar, Pritam Halder, Aditi Sen De

Published Jan 20, 2026• 5 citations
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Abstract

Building on the recently developed quantum state texture resource theory, we exhibit that the difference between maximum and minimum textures is a valid purity monotone in any dimension and provide a lower bound for existing purity measures. We introduce a texture-based resource monotone applicable across general convex resource theories, encompassing quantum coherence, non-stabilizerness, and entanglement. In particular, we propose the notion of non-local texture, which corresponds to the geometric measure of bipartite and multipartite entanglement in pure states. Furthermore, we demonstrate that the texture of the entire ground state or its subsystems can effectively signal quantum phase transitions in the Ising chain under both transverse and longitudinal magnetic fields, offering a powerful tool for characterizing quantum criticality.

DOI
10.1103/y2wz-ypln

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Building on the recently developed quantum state texture resource theory, we exhibit that the difference between maximum and minimum textures is a valid purity monotone in any dimension and provide a lower bound for existing purity measures. We introduce a texture-based resource monotone applicable across general convex resource theories, encompassing quantum coherence, non-stabilizerness, and entanglement. In particular, we propose the notion of non-local texture, which corresponds to the geometric measure of bipartite and multipartite entanglement in pure states. Furthermore, we demonstrate that the texture of the entire ground state or its subsystems can effectively signal quantum phase transitions in the Ising chain under both transverse and longitudinal magnetic fields, offering a powerful tool for characterizing quantum criticality.
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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.
We investigate the role of quantum state texture in dynamical quantum phase transitions by establishing a direct connection between critical nonequilibrium dynamics and the recently introduced notion of rugosity, a measure of quantum state texture. Considering a generic quench protocol, we analyze both standard formulations of dynamical quantum phase transitions. For type-I transitions, characterized through the long-time behavior of a dynamical order parameter, we show that the time-averaged rugosity, evaluated in the eigenbasis of the pre-quench Hamiltonian, exhibits an order-parameter-like behavior across the transition. In the Lipkin-Meshkov-Glick model, this behavior is traced back to the underlying semiclassical structure, where crossing the excited-state quantum phase transition separatrix controls the redistribution of the quantum state over the pre-quench energy basis. We further demonstrate that the response function associated with the time-averaged rugosity develops a pronounced critical peak whose maximum grows algebraically with the system size, providing quantitative finite-size evidence of its sensitivity to the dynamical critical point. For type-II transitions, characterized by nonanalyticities in the Loschmidt rate function, we establish an exact connection with rugosity. For a suitable choice of basis, the rate function is exactly given by the density of rugosity, establishing a model-independent equivalence. Moreover, we show that even in physically motivated bases, such as the pre-quench energy eigenbasis, rugosity provides clear signatures of dynamical criticality. Our results establish rugosity as a sensitive probe of dynamical quantum phase transitions while highlighting its role as a basis-dependent measure of quantum state texture, thereby providing an information-theoretic perspective on nonequilibrium quantum critical phenomena.
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.