aiqbench analysis
This paper advances fundamental quantum information theory by establishing rigorous convexity and monotonicity properties for a novel family of conditional entropies derived from trace functionals. The work provides essential mathematical tools, such as data-processing inequalities and chain rules, that underpin the operational significance required for future developments in quantum communication protocols and error correction schemes.
Quantum conditional entropies from convex trace functionals
arXiv:2410.21976v4 Announce Type: replace Abstract: We study geometric properties of trace functionals that generalize those in [Zhang, Adv. Math. 365:107053 (2020)], arising from a novel family of conditional entropies with applications in quantum information. Building on new convexity results for these functionals, we establish data-processing inequalities and additivity properties for our entropies, demonstrating their operational significance. We further prove completeness under duality, chain rules, and various monotonicity properties for this family. Our proofs draw on tools from complex interpolation theory, multivariate Araki--Lieb and Lieb--Thirring inequalities, variational characterizations of trace functionals, and spectral pinching techniques.
Abstract:We study geometric properties of trace functionals that generalize those in [Zhang, Adv. Math. 365:107053 (2020)], arising from a novel family of conditional entropies with applications in quantum information. Building on new convexity results for these functionals, we establish data-processing inequalities and additivity properties for our entropies, demonstrating their operational significance. We further prove completeness under duality, chain rules, and various monotonicity properties for this family. Our proofs draw on tools from complex interpolation theory, multivariate Araki--Lieb and Lieb--Thirring inequalities, variational characterizations of trace functionals, and spectral pinching techniques.
arXiv:2410.21976 [quant-ph]
(or arXiv:2410.21976v4 [quant-ph] for this version)
Full text under the publisher's open licence · 97 words
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