Optimal Approximate Quantum Conversion from a Taut-String Principle in Majorization-Based Resource Theories
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 α-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.
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BibTeX
@misc{meroi2026optimal,
title = {{Optimal Approximate Quantum Conversion from a Taut-String Principle in Majorization-Based Resource Theories}},
author = {Franco Meroi and Cesar Massri and Marcelo Losada and Guido Bellomo and Gustavo Martin Bosyk},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.28015},
eprint = {2610.28015},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.28015},
}
RIS
TY - UNPB
TI - Optimal Approximate Quantum Conversion from a Taut-String Principle in Majorization-Based Resource Theories
AU - Franco Meroi
AU - Cesar Massri
AU - Marcelo Losada
AU - Guido Bellomo
AU - Gustavo Martin Bosyk
PY - 2026
DA - 2026/10/20
PB - arXiv
DO - 10.48550/arxiv.2610.28015
UR - https://arxiv.org/abs/2610.28015
AB - 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 α-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.
ER -