The entanglement of purification is not additive

arXiv:2609.29539 · quant-ph · Submitted 2026-08-25 · Read on arXiv

quant-ph

Submitted: 2026-08-25

Updated: 2026-08-25

Comments: 24 pages; verification artifact archived at doi:10.5281/zenodo.22097511

License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/

Terminology

• Entanglement — 30× in this paper · explained in 3 episodes
• Trace — 13× in this paper · explained in 2 episodes
• Additivity — 11× in this paper · explained in 1 episode
• Verifier — 9× in this paper · explained in 2 episodes
• Verification — 5× in this paper · explained in 2 episodes
• Stiefel manifold — 3× in this paper · explained in 2 episodes
• Trace Distance — 3× in this paper · explained in 3 episodes
• Entanglement Entropy — 1× in this paper · explained in 2 episodes
• Regularization — 1× in this paper · explained in 3 episodes
• Robustness — 1× in this paper · explained in 5 episodes
• Superadditivity — 1× in this paper · explained in 2 episodes

Sources

• The entanglement of purification
• Non-Additivity of the Entanglement of Purification (Beyond Reasonable Doubt)
• Uncertainty, Monogamy, and Locking of Quantum Correlations
• Symmetric Extension of Two-Qubit States
• Monogamy, polygamy, and other properties of entanglement of purification
• Strong Converse Bounds for Compression of Mixed States
• Additivity Results for the R'enyi-2 Entanglement of Purification
• Superadditivity of communication capacity using entangled inputs
• Holographic Entanglement of Purification

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