Quantum Resource Theories beyond Convexity

A 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.

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Publication Details

Journal
Quantum
Published
2026-05-13
DOI
https://doi.org/10.22331/q-2026-05-13-2104
Citations
1
Primary Topic
Quantum Mechanics and Applications
Type
preprint
Field-Weighted Citation Impact
0.00

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preprint

Quantum Resource Theories beyond Convexity

Roberto Salazar, Grzegorz Rajchel-Mieldzioć, Ricard Ravell Rodríguez, Jakub Czartowski et al.
1 citations
Quantum
Quantum Mechanics and Applications
preprint

Quantum Resource Theories beyond Convexity

Roberto Salazar, Grzegorz Rajchel-Mieldzioć, Ricard Ravell Rodríguez, Jakub Czartowski, Karol Życzkowski, Paweł Horodecki
preprint en
1 citations

Abstract

A 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.

QuantumVol. 10
Jagiellonian University (PL), Nanyang Technological University (SG), Institute of Photonic Sciences (ES), University of Malta (MT), Center for Theoretical Physics (PL), University of Gdańsk (PL), Institute for Cross-Disciplinary Physics and Complex Systems (ES), Institute of Advanced Manufacturing Technology (PL), Polish Academy of Sciences (PL)
European Commission, Fundacja na rzecz Nauki Polskiej, Narodowe Centrum Nauki, Narodowym Centrum Nauki, QuantERA, HORIZON EUROPE European Innovation Council
Openalex Percentile: Top 100%
Quantum Mechanics and Applications
DOIOpen Access PDFOpenAlex
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