Complete Classification of Reversible Entanglement Transformations of Two Qutrits

Wei Song; Xiao-Lan Zong; Ming Yang

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arXiv · 2610.05234

Complete Classification of Reversible Entanglement Transformations of Two Qutrits

Wei Song·Xiao-Lan Zong·Ming Yang

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Abstract

Suppose Alice and Bob can transform one shared mixed state into another by local operations and classical communication, and can also recover the first state from the second. What can change in such a conversion? We give a complete classification of reversible conversions between two-qutrit states. We consider exact deterministic LOCC transformations of a single copy, allowing finite protocols and the countable protocols specified here. Local flags are known to allow a separable part to be replaced by local preparation while an entangled block is retained. We prove that such a decomposition is necessary for two mutually convertible entangled states that are not locally unitarily equivalent. The two parts are distinguishable by local measurements. The entangled blocks have the same weight and are locally unitarily equivalent after normalization. Each entangled state has a unique smallest retained block. Two entangled states are reversibly convertible if and only if these unnormalized blocks are locally unitarily equivalent. For a state with negative partial transpose, the smallest block can be found using the negative eigenspace of its partial transpose and at most three matrix zero tests.

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BibTeX RIS

Wei Song, Xiao-Lan Zong, Ming Yang. 2026-10-04. Complete Classification of Reversible Entanglement Transformations of Two Qutrits. https://arxiv.org/abs/2610.05234

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