Typical Entanglement of Superpositions

• URL: http://arxiv.org/abs/2607.06474v1
• Date: Tue, 07 Jul 2026 16:30:33 GMT
• Title: Typical Entanglement of Superpositions
• Abstract summary: We investigate entanglement properties inherent to superpositions of randomized states.<n>An $m$-fold superposition of typical states may be classified into two distinct entanglement classes.<n>We show that an exponentially large number of superpositions is required to transition from the sub-maximally entangled class to maximal entanglement.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We investigate universal entanglement properties inherent to superpositions of randomized states. We find that an $m$-fold superposition of typical states may be classified into two distinct entanglement classes via the 2nd Rényi entropy density $s_2$. The maximally entangled regime is defined by $s_2 \sim \ln (2)$, for which superposition adds no additional entanglement. The sub-maximally entangled regime, $s_2<\ln 2$, instead constrains the reduced density matrices of independent components to be orthogonal in the thermodynamic limit, which fixes the entanglement of the superposition to a logarithmic enhancement $ΔS(m)=\ln (m)$. As a consequence, an exponentially large number of superpositions is required to transition from the sub-maximally entangled class to maximal entanglement. We explicitly calculate $s_2$ and the logarithmic enhancement, and demonstrate orthogonality for two canonical examples of the sub-maximally entangled regime (superpositions of pure Gaussian states and of random matrix-product states). We also examine the entanglement of superpositions of random stabilizer states, and discuss their relaxation to the Haar limit.

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