Rényi Entanglement of Purification Is Non-additive

• URL: http://arxiv.org/abs/2608.28897v1
• Date: Fri, 28 Aug 2026 21:54:33 GMT
• Title: Rényi Entanglement of Purification Is Non-additive
• Abstract summary: Entanglement of purification is a fundamental measure of total correlations whose additivity remains unresolved.<n>We study its additivity for classical states on two qubits at different Rényi orders.
• Score: 3.151184728006369
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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 $α\in[0,1)$, 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 $α\in[2,\infty]$ we prove additivity under tensor products within this family. The interval $α\in[1,2)$, including the von Neumann case $α=1$, remains open, and we conjecture additivity there throughout the same family.

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