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arXiv · 1303.4209

Typical Entanglement

Fabio Deelan Cunden·Paolo Facchi·Giuseppe Florio·Saverio Pascazio
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Abstract

Let a pure state \psi be chosen randomly in an NM-dimensional Hilbert space, and consider the reduced density matrix \rho of an N-dimensional subsystem. The bipartite entanglement properties of \psi are encoded in the spectrum of \rho. 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.

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Fabio Deelan Cunden, Paolo Facchi, Giuseppe Florio, Saverio Pascazio. 2013-03-18. Typical Entanglement. https://doi.org/10.1140/epjp/i2013-13048-6

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