aiqbench analysis
This research establishes the non-additivity of Rényi entanglement of purification for classical states on two qubits when the order $\alpha$ is in the range $[0,1)$, while proving additivity for $\alpha \ge 2$. The study resolves specific optimization problems within these families and leaves the interval $[1,2)$, including the von Neumann case, as an open conjecture. These findings advance the theoretical understanding of correlation measures fundamental to quantum information theory and quantum computing architectures.
R\'enyi Entanglement of Purification Is Non-additive
arXiv:2608.28897v1 Announce Type: new 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 R\'enyi orders. For every $\alpha\in[0,1)$, 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 R\'enyi 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 $\alpha\in[2,\infty]$ we prove additivity under tensor products within this family. The interval $\alpha\in[1,2)$, including the von Neumann case $\alpha=1$, remains open, and we conjecture additivity there throughout the same family.
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 $\alpha\in[0,1)$, 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 $\alpha\in[2,\infty]$ we prove additivity under tensor products within this family. The interval $\alpha\in[1,2)$, including the von Neumann case $\alpha=1$, remains open, and we conjecture additivity there throughout the same family.
Quantum Physics (quant-ph); Information Theory (cs.IT)
arXiv:2608.28897 [quant-ph]
(or arXiv:2608.28897v1 [quant-ph] for this version)
https://doi.org/10.48550/arXiv.2608.28897 Focus to learn more arXiv-issued DOI via DataCite (pending registration)
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