Typical Entanglement

Abstract

Let a pure state ψbe chosen randomly in an NM-dimensional Hilbert space, and consider the reduced density matrix ρof an N-dimensional subsystem. The bipartite entanglement properties of ψare encoded in the spectrum of ρ. By means of a saddle point method and using a "Coulomb gas" model for the eigenvalues, we obtain the typical spectrum of reduced density matrices. We consider the cases of an unbiased ensemble of pure states and of a fixed value of the purity. We finally obtain the eigenvalue distribution by using a statistical mechanics approach based on the introduction of a partition function.

15 pages, 4 figures

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Cited by in corpus (8)

• Random pure states: quantifying bipartite entanglement beyond the linear statistics
• Symmetry-resolved Page curves
• Entanglement Typicality
• Generic aspects of the resource theory of quantum coherence
• Inhibition of spread of typical bipartite and genuine multiparty entanglement in response to disorder
• Polarized ensembles of random pure states
• Non-Abelian entanglement asymmetry in random states
• Phase diagram of bipartite entanglement