Rényi Entanglement of Purification Is Non-additive
Abstract
Entanglement of purification is a fundamental measure of total correlations whose additivity remains unresolved. We study its additivity for classical states on two qubits at different Rényi orders. For every α∈[0,1), we prove nonadditivity within this family, witnessed by two copies of a single state. We first solve the one-copy optimization exactly for the entire family at every Rényi order. We then restrict the two-copy optimization to a natural finite set of purifications and exhibit one whose entropy is strictly below the product value. In contrast, for α∈[2,∞] we prove additivity under tensor products within this family. The interval α∈[1,2), including the von Neumann case α=1, remains open, and we conjecture additivity there throughout the same family.
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BibTeX
@misc{negari2026rényi,
title = {{Rényi Entanglement of Purification Is Non-additive}},
author = {Amir-Reza Negari and Zahra Baghali Khanian},
howpublished = {arXiv},
year = {2026},
month = aug,
doi = {10.48550/arxiv.2608.28897},
eprint = {2608.28897},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2608.28897},
}
RIS
TY - UNPB
TI - Rényi Entanglement of Purification Is Non-additive
AU - Amir-Reza Negari
AU - Zahra Baghali Khanian
PY - 2026
DA - 2026/08/28
PB - arXiv
DO - 10.48550/arxiv.2608.28897
UR - https://arxiv.org/abs/2608.28897
AB - Entanglement of purification is a fundamental measure of total correlations whose additivity remains unresolved. We study its additivity for classical states on two qubits at different Rényi orders. For every α∈[0,1), we prove nonadditivity within this family, witnessed by two copies of a single state. We first solve the one-copy optimization exactly for the entire family at every Rényi order. We then restrict the two-copy optimization to a natural finite set of purifications and exhibit one whose entropy is strictly below the product value. In contrast, for α∈[2,∞] we prove additivity under tensor products within this family. The interval α∈[1,2), including the von Neumann case α=1, remains open, and we conjecture additivity there throughout the same family.
ER -