Entanglement is not only the most intriguing feature of quantum mechanics,
but also a key resource in quantum information science. The entanglement
content of random pure quantum states is almost maximal; such states find
applications in various quantum information protocols. The preparation of a
random state or, equivalently, the implementation of a random unitary operator,
requires a number of elementary one- and two-qubit gates that is exponential in
the number n_q of qubits, thus becoming rapidly unfeasible when increasing n_q.
On the other hand, pseudo-random states approximating to the desired accuracy
the entanglement properties of true random states may be generated efficiently,
that is, polynomially in n_q. In particular, quantum chaotic maps are efficient
generators of multipartite entanglement among the qubits, close to that
expected for random states. This review discusses several aspects of the
relationship between entanglement, randomness and chaos. In particular, I will
focus on the following items: (i) the robustness of the entanglement generated
by quantum chaotic maps when taking into account the unavoidable noise sources
affecting a quantum computer; (ii) the detection of the entanglement of
high-dimensional (mixtures of) random states, an issue also related to the
question of the emergence of classicality in coarse grained quantum chaotic
dynamics; (iii) the decoherence induced by the coupling of a system to a
chaotic environment, that is, by the entanglement established between the
system and the environment.Comment: Review paper, 40 pages, 7 figures, added reference
