aiqbench analysis
This paper establishes a unified geometric framework using taut-string constructions to solve optimal approximate state conversion across major quantum resource theories, including entanglement and coherence. By reducing complex optimization problems involving various distinguishability measures to four elementary principles, the work provides a fundamental theoretical advance for quantum information science.
Optimal Approximate Quantum Conversion from a Taut-String Principle in Majorization-Based Resource Theories
arXiv:2610.28015v1 Announce Type: new Abstract: Optimal approximate state conversion is a fundamental task in quantum resource theories, yet existing solutions are largely tailored to specific distinguishability measures and resource theories. We show that every optimal approximate-conversion problem in the three paradigmatic majorization-based quantum resource theories of non-uniformity, bipartite pure-state entanglement, and pure-state coherence reduces exactly to one of only four elementary taut-string constructions. This holds for problems generated by Schur-convex spectral distances and by a broad family of quantum divergences satisfying a natural reduction property with respect to the corresponding equivalence group. The resulting framework encompasses a broad class of physically relevant distinguishability measures, including the trace distance, all unitarily invariant norms, quantum relative entropy, maximal quantum $f$-divergences, and the $\alpha$-$z$ R\'enyi relative entropies. The increment vector of the corresponding taut string completely determines both the optimal approximation error and a canonical optimal state. Our results establish a common geometric framework for approximate quantum resource conversion, revealing that a broad class of seemingly different optimization problems is governed by the same taut-string geometric principle.
Abstract:Optimal approximate state conversion is a fundamental task in quantum resource theories, yet existing solutions are largely tailored to specific distinguishability measures and resource theories. We show that every optimal approximate-conversion problem in the three paradigmatic majorization-based quantum resource theories of non-uniformity, bipartite pure-state entanglement, and pure-state coherence reduces exactly to one of only four elementary taut-string constructions. This holds for problems generated by Schur-convex spectral distances and by a broad family of quantum divergences satisfying a natural reduction property with respect to the corresponding equivalence group. The resulting framework encompasses a broad class of physically relevant distinguishability measures, including the trace distance, all unitarily invariant norms, quantum relative entropy, maximal quantum $f$-divergences, and the $\alpha$-$z$ Rényi relative entropies. The increment vector of the corresponding taut string completely determines both the optimal approximation error and a canonical optimal state. Our results establish a common geometric framework for approximate quantum resource conversion, revealing that a broad class of seemingly different optimization problems is governed by the same taut-string geometric principle.
arXiv:2610.28015 [quant-ph]
(or arXiv:2610.28015v1 [quant-ph] for this version)
https://doi.org/10.48550/arXiv.2610.28015 Focus to learn more arXiv-issued DOI via DataCite (pending registration)
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Full text under the publisher's open licence · 260 words