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arXiv · 2608.05274

Relative entropy of entanglement of Haar random states

Takato Mori·Beni Yoshida
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Abstract

We determine the relative entropy of entanglement of a bipartite mixed state $\rho_{AB}$ obtained by tracing out one subsystem of a tripartite Haar-random pure state $|\psi\rangle_{ABC}$, finding $E_R(\rho_{AB})=\log\frac{d_Ad_B}{\max(d_A,d_B,d_C)}+O(1)$. Equivalently, the relative entropy of entanglement nearly saturates the smaller of the entanglement of formation $E_F(\rho_{AB})$ and the mutual information $I(A:B)$. The upper bound is achieved by an explicit separable state obtained through one-sided Schmidt dephasing, which is therefore approximately closest.

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Takato Mori, Beni Yoshida. 2026-08-05. Relative entropy of entanglement of Haar random states. https://arxiv.org/abs/2608.05274

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