Relative entropy of entanglement of Haar random states

• URL: http://arxiv.org/abs/2608.05274v1
• Date: Wed, 05 Aug 2026 18:00:00 GMT
• Title: Relative entropy of entanglement of Haar random states
• Abstract summary: We find the relative entropy of entanglement of a bipartite mixed state $_AB$ obtained by tracing out one subsystem.<n>The entropy of entanglement nearly saturates the smaller of the entanglement of formation $E_F(_AB)$ and the mutual information $I(A:B)$.
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• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We determine the relative entropy of entanglement of a bipartite mixed state $ρ_{AB}$ obtained by tracing out one subsystem of a tripartite Haar-random pure state $|ψ\rangle_{ABC}$, finding $E_R(ρ_{AB})=\log\frac{d_Ad_B}{\max(d_A,d_B,d_C)}+O(1)$. Equivalently, the relative entropy of entanglement nearly saturates the smaller of the entanglement of formation $E_F(ρ_{AB})$ 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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