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arXiv · 2610.28015

Optimal Approximate Quantum Conversion from a Taut-String Principle in Majorization-Based Resource Theories

Franco Meroi·Cesar Massri·Marcelo Losada·Guido Bellomo·Gustavo Martin Bosyk
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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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Franco Meroi, Cesar Massri, Marcelo Losada, Guido Bellomo, Gustavo Martin Bosyk. 2026-10-20. Optimal Approximate Quantum Conversion from a Taut-String Principle in Majorization-Based Resource Theories. https://arxiv.org/abs/2610.28015

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