Entanglement in random pure states: spectral density and average von Neumann entropy

Abstract

Quantum entanglement plays a crucial role in quantum information, quantum\nteleportation and quantum computation. The information about the entanglement\ncontent between subsystems of the composite system is encoded in the Schmidt\neigenvalues. We derive here closed expressions for the spectral density of\nSchmidt eigenvalues for all three invariant classes of random matrix ensembles.\nWe also obtain exact results for average von Neumann entropy. We find that\nmaximum average entanglement is achieved if the system belongs to the\nsymplectic invariant class.\n