A brief introduction to multipartite entanglement

Abstract

A concise introduction to quantum entanglement in multipartite systems is presented. We review entanglement of pure quantum states of three--partite systems analyzing the classes of GHZ and W states and discussing the monogamy relations. Special attention is paid to equivalence with respect to local unitaries and stochastic local operations, invariants along these orbits, momentum map and spectra of partial traces. We discuss absolutely maximally entangled states and their relation to quantum error correction codes. An important case of a large number of parties is also analysed and entanglement in spin systems is briefly reviewed.

arXiv comment37 pages with 13 figures. Preprint based on a new chapter written to the second edition of the book "Geometry of Quantum States. An introduction to Quantum Entanglement", CUP, Cambridge, to appear in 2017

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• SU(N)1 Chern-Simons theory, the Clifford group, and Entropy Cone