Let a pure state vertical bar psi > be chosen randomly in an NM-dimensional Hilbert space, and consider the reduced density matrix rho(A) of an N-dimensional subsystem. The bipartite entanglement properties of vertical bar psi > are encoded in the spectrum of rho(A). 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.
Typical entanglement
Cunden FD;FACCHI, PAOLO;PASCAZIO, Saverio
2013-01-01
Abstract
Let a pure state vertical bar psi > be chosen randomly in an NM-dimensional Hilbert space, and consider the reduced density matrix rho(A) of an N-dimensional subsystem. The bipartite entanglement properties of vertical bar psi > are encoded in the spectrum of rho(A). 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.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
