Entanglement of purification for Werner states: canonical purification and nonadditivity

@misc{khanian2026entanglement,
  title = {{Entanglement of purification for Werner states: canonical purification and nonadditivity}},
  author = {Zahra Baghali Khanian and Amir-Reza Negari},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.03630},
  eprint = {2610.03630},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.03630},
}

TY  - UNPB
TI  - Entanglement of purification for Werner states: canonical purification and nonadditivity
AU  - Zahra Baghali Khanian
AU  - Amir-Reza Negari
PY  - 2026
DA  - 2026/10/02
PB  - arXiv
DO  - 10.48550/arxiv.2610.03630
UR  - https://arxiv.org/abs/2610.03630
AB  - We prove that the von Neumann entanglement of purification is nonadditive. For two-qubit Werner states W(f) with singlet weight 1/64≤ f≤1/4, we show that canonical purification is globally optimal: its entanglement, also known as reflected entropy, gives the exact entanglement of purification. In contrast, the regularized entanglement of purification lies strictly below the reflected entropy for 0<f<f_∗, where f_∗≈0.017. Together, these results establish nonadditivity throughout 1/64≤ f<f_∗. Our canonical-optimality proof generalizes the proof in [1], which established Rényi nonadditivity for 0≤α<1 using classical two-qubit states. We thus resolve the additivity question at α=1. Remarkably, nonadditivity is again witnessed by separable states and no entanglement in the underlying states is required.
ER  -