Zahra Khanian

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We establish nonadditivity of entanglement of purification, resolving a longstanding
additivity question in quantum Shannon theory. This fundamental measure captures total cor-
relations, and its regularization determines the entanglement cost of state preparation with a
vanishing quantum communication rate. A separable two-qubit state already exhibits a strict
collective advantage: even in this elementary setting, the asymptotic cost is strictly smaller
than the single-copy entanglement of purification. The phenomenon extends to every Rényi
order 0 ≤ α < 1, where we construct classical two-qubit states with explicit two-copy violations.
Thus, collective savings arise even without entanglement and, below order one, without non-
classical correlations. We also identify robust regimes of additivity: classical two-qubit states
are additive with arbitrary classical partners at orders α ≥ 2, and a Rényi-2 multiplicativity cri-
terion establishes additivity for states associated with depolarizing and transpose-depolarizing
channels and their complementary channels. Beyond establishing these results, we uncover
structural mechanisms behind both behaviors. Collective sign choices can reshape purification
spectra to reduce entropy, while norm inequalities and algebraic multiplicativity conditions can
enforce the optimality of product purifications.

This talk is based on the following preprints:
https://arxiv.org/abs/2610.03630,  https://arxiv.org/abs/2608.28897,  https://arxiv.org/abs/2605.15439

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IQC Waterloo
0.03
Contact: Andreas Winter