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Quantum Resource Theories beyond Convexity

Quantum Science and Technology (arXiv overlay)

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A team of researchers including Roberto Salazar and Paweł Horodecki introduced a new framework for quantum resource theories using star-shaped geometric sets, moving beyond traditional convexity assumptions. This approach captures quantum properties like discord and non-Markovianity that standard theories cannot address. The study demonstrates that non-linear witnesses outperform linear ones in detecting quantum resources, improving tasks like correlated quantum discrimination and testing quantum combs. These tools enhance performance in previously challenging scenarios. Applications span quantum dynamics, including estimating non-Markovianity and analyzing unistochastic matrices, with implications for high-energy physics and CP-symmetry violation studies. The framework unifies disparate quantum phenomena. Star-shaped sets generalize convex theories, offering operational interpretations and quantifiers for resources like total correlations in composite systems. This geometric flexibility expands the scope of quantum information theory. The work provides universal free operations and resource measures, proving advantages in static and dynamical quantum tasks. It bridges gaps between theoretical models and practical quantum technologies.

Quantum Resource Theories beyond Convexity

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AbstractA class of quantum resource theories, based on non-convex star-shape sets, presented in this work captures the key quantum properties that cannot be studied by standard convex theories. We provide operational interpretations for a resource of this class and demonstrate its advantage to improve performance of correlated quantum discrimination tasks and testing of quantum combs. Proposed techniques provide useful tools to describe quantum discord, total correlations in composite quantum systems and to estimate the degree of non-Markovianity of an analyzed quantum dynamics. Other applications include the problem of unistochasticity of a given bistochastic matrix, with relevance for quantization of classical dynamics and studies of violation of CP-symmetry in high energy physics. In all these cases, the non-linear witnesses introduced here outperform the standard linear witnesses. Importance of our findings for quantum information theory is also emphasized.Featured image: Echoing the geometry of historical star fortresses, our work develops star resource theories, where star-shaped geometric structures provide a natural way to quantify quantum resources.Popular summaryQuantum resource theories provide a general framework for identifying and quantifying useful physical features, such as entanglement or coherence. Most existing resource theories assume that the set of free objects is convex, meaning that any probabilistic mixture of free objects is again free. While this assumption is mathematically convenient, it excludes important scenarios in which the free set is naturally non-convex, including quantum discord, total correlations, and non-Markovian processes. In this work, we introduce a broad class of star resource theories, in which the free set is only required to be star-shaped. This geometric condition includes all convex resource theories as a special case, while also covering relevant non-convex examples. We construct resource quantifiers for this setting, prove universal operational interpretations for them, and identify classes of free operations that apply across the framework. The resulting nonlinear witnesses can detect resources in situations where standard linear methods are ineffective. We illustrate the framework with several applications, including quantum discord, total correlations, non-unistochasticity, and non-Markovianity. These examples show that moving beyond convexity enables the formulation of meaningful, operationally useful resource theories for quantum features that were previously difficult to treat within a unified framework.► BibTeX data@article{Salazar2026quantumresource, doi = {10.22331/q-2026-05-13-2104}, url = {https://doi.org/10.22331/q-2026-05-13-2104}, title = {Quantum {R}esource {T}heories beyond {C}onvexity}, author = {Salazar, Roberto and Czartowski, Jakub and Ravell Rodr{\'{i}}guez, Ricard and Rajchel-Mieldzio{\'{c}}, Grzegorz and Horodecki, Pawe{\l{}} and {\.{Z}}yczkowski, Karol}, journal = {{Quantum}}, issn = {2521-327X}, publisher = {{Verein zur F{\"{o}}rderung des Open Access Publizierens in den Quantenwissenschaften}}, volume = {10}, pages = {2104}, month = may, year = {2026} }► References [1] C. H. Bennett. ``A resource-based view of quantum information''. Quantum Inf. Comput. 4, 460–466 (2004). https://doi.org/10.26421/QIC4.6-7-5 [2] I. Devetak, A. W. Harrow, and A. J. 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University of California Press (1951). url: projecteuclid.org/euclid.bsmsp/1200500249. https://projecteuclid.org/euclid.bsmsp/1200500249Cited byCould not fetch Crossref cited-by data during last attempt 2026-05-13 06:52:52: Could not fetch cited-by data for 10.22331/q-2026-05-13-2104 from Crossref. This is normal if the DOI was registered recently. Could not fetch ADS cited-by data during last attempt 2026-05-13 06:52:58: No response from ADS or unable to decode the received json data when getting the list of citing works.This Paper is published in Quantum under the Creative Commons Attribution 4.0 International (CC BY 4.0) license. Copyright remains with the original copyright holders such as the authors or their institutions. AbstractA class of quantum resource theories, based on non-convex star-shape sets, presented in this work captures the key quantum properties that cannot be studied by standard convex theories. We provide operational interpretations for a resource of this class and demonstrate its advantage to improve performance of correlated quantum discrimination tasks and testing of quantum combs. Proposed techniques provide useful tools to describe quantum discord, total correlations in composite quantum systems and to estimate the degree of non-Markovianity of an analyzed quantum dynamics. Other applications include the problem of unistochasticity of a given bistochastic matrix, with relevance for quantization of classical dynamics and studies of violation of CP-symmetry in high energy physics. In all these cases, the non-linear witnesses introduced here outperform the standard linear witnesses. Importance of our findings for quantum information theory is also emphasized.Featured image: Echoing the geometry of historical star fortresses, our work develops star resource theories, where star-shaped geometric structures provide a natural way to quantify quantum resources.Popular summaryQuantum resource theories provide a general framework for identifying and quantifying useful physical features, such as entanglement or coherence. Most existing resource theories assume that the set of free objects is convex, meaning that any probabilistic mixture of free objects is again free. While this assumption is mathematically convenient, it excludes important scenarios in which the free set is naturally non-convex, including quantum discord, total correlations, and non-Markovian processes. In this work, we introduce a broad class of star resource theories, in which the free set is only required to be star-shaped. This geometric condition includes all convex resource theories as a special case, while also covering relevant non-convex examples. We construct resource quantifiers for this setting, prove universal operational interpretations for them, and identify classes of free operations that apply across the framework. The resulting nonlinear witnesses can detect resources in situations where standard linear methods are ineffective. We illustrate the framework with several applications, including quantum discord, total correlations, non-unistochasticity, and non-Markovianity. These examples show that moving beyond convexity enables the formulation of meaningful, operationally useful resource theories for quantum features that were previously difficult to treat within a unified framework.► BibTeX data@article{Salazar2026quantumresource, doi = {10.22331/q-2026-05-13-2104}, url = {https://doi.org/10.22331/q-2026-05-13-2104}, title = {Quantum {R}esource {T}heories beyond {C}onvexity}, author = {Salazar, Roberto and Czartowski, Jakub and Ravell Rodr{\'{i}}guez, Ricard and Rajchel-Mieldzio{\'{c}}, Grzegorz and Horodecki, Pawe{\l{}} and {\.{Z}}yczkowski, Karol}, journal = {{Quantum}}, issn = {2521-327X}, publisher = {{Verein zur F{\"{o}}rderung des Open Access Publizierens in den Quantenwissenschaften}}, volume = {10}, pages = {2104}, month = may, year = {2026} }► References [1] C. H. Bennett. ``A resource-based view of quantum information''. Quantum Inf. Comput. 4, 460–466 (2004). https://doi.org/10.26421/QIC4.6-7-5 [2] I. Devetak, A. W. Harrow, and A. J. 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Quantum Resource Theories beyond Convexity

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