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Résumé |
Entanglement is probably the most fundamental and intriguing feature
of quantum theory. A well-known measure of entanglement
between two parts of a system is the Von Neumann en-
tropy (or more generally the Renyi entropy) of either subsystem, which is
the quantum version of the classical Shannon entropy.
In a large system where the Hamiltonian is not known precisely, the wave-
function can be modelled as a random superposition of the basis states: a random state.
I will show how one can compute
analytically (using a Coulomb gas method)
the probability distribution of the Renyi entropy
for a random pure state of a large bipartite quantum system.
In particular, we find that this distribution changes shape twice, at
two critical values. This is the consequence of two phase transitions in the corresponding charge density of the Coulomb gas. |
