Quantum

R\'enyi-2 entanglement of purification of the symmetric Werner state

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Briefings

A 2026 paper by R'enyi et al. determines the exact R'enyi-2 entanglement of purification for the symmetric Werner state in all dimensions d≥2, yielding log2(4d(d+1)/(d^2+3d+4)). The study establishes additivity for tensor powers and finite products of such states, proving the canonical purification is globally optimal even with unrestricted auxiliary systems. Perturbation analysis confirms continuity of the optimal value at the symmetric endpoint, with a sharp square root order variation in purity while the canonical purification remains asymptotically optimal.

Key points

• The paper provides an exact formula for the R'enyi-2 entanglement of purification of the symmetric Werner state in every local dimension d≥2.
• Additivity is proven for tensor powers and finite products of symmetric Werner states with different local dimensions, with the canonical purification achieving these values globally.

Context

This research advances quantum information theory by characterizing the entanglement of purification for a specific class of mixed states, providing a benchmark for quantum state discrimination and purification protocols.

Limitations

The study is preprint arXiv:2611.00144v1 and lacks peer review; results are subject to revision. Evidence is limited to the abstract and provided equations, with no experimental data or additional background context supplied.

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