We give a review on entanglement purification for bipartite and multipartite quantum states, with the main focus on theoretical work carried out by our group in the last couple of years. We discuss entanglement purification in the context of quantum communication, where we emphasize its close relation to quantum error correction. Various bipartite and multipartite entanglement purification prot...

We consider entanglement witnesses arising from positive linear maps which generate exposed extremal rays. We show that every entanglement can be detected by one of these witnesses, and this witness detects a unique set of entanglement among those. Therefore, they provide a minimal set of witnesses to detect all entanglement in a sense. Furthermore, if those maps are indecomposable then they de...

Electron–electron correlation in quantum chemistry calculations can be analysed in terms of entanglement between electrons. Two exactly solvable models: two fixed spin-1/2 particles and two-electron two-site Hubbard model are used to define and discuss the entanglement as a function of the system parameters. Ab initio configuration interaction calculation for entanglement is presented for the H...

We study evolution of entanglement of two two-level atoms in the presence of dissi-pation caused by spontaneous emission. We find explicit formulas for the amount of entanglement as a function of time, in the case of destruction of the initial entanglement and possible creation of a transient entanglement between atoms. We also discuss how spontaneous emission influences nonlocality of states e...

The ground state entanglement of the system, both in discrete-time and continuous-time cases, is quantified through the linear entropy. The result shows that the entanglement increases as the interaction between the particles increases in both time scales. It is also found that the strength of the harmonic potential affects the formation rate of the entanglement of the system. The different fea...

Multipartite entanglement is used for quantum information applications, such as building multipartite quantum communications. Generally, generation of multipartite entanglement is based on a complex beam-splitter network. Here, based on the spatial freedom of light, we experimentally demonstrated spatial quadripartite continuous variable entanglement among first-order Hermite-Gaussian modes usi...

We outline the basic questions that are being studied in any theory of entanglement. Following a a brief review of some of the main achievements of entanglement theory for finite-dimensional systems such as qubits, we will then consider entanglement in infinite-dimensional systems. Asking for a theory of entanglement in such systems under experimentally feasible operations leads to the developm...

The AdS/CFT correspondence relates quantum entanglement between boundary Conformal Field Theories and geometric connections in the dual asymptotically Antide Sitter space-time. We consider entangled states in the n−fold tensor product of a 1+1 dimensional CFT Hilbert space defined by the Euclidean path integral over a Riemann surface with n holes. In one region of moduli space, the dual bulk st...

In this thesis we discuss the general spatial structure of quantum entanglement in local many-body systems. A central theme is the organizing power of the renormalization group for thinking about many-body entanglement. We argue that the coarse structure of entanglement across of wide variety of systems, from gapped topological phases to gapless Fermi liquids in a variety of dimensions, can all...

All our former experience with application of quantum theory seems to say: what is predicted by quantum formalism must occur in laboratory. But the essence of quantum formalism — entanglement, recognized by Einstein, Podolsky, Rosen and Schrödinger — waited over 70 years to enter to laboratories as a new resource as real as energy. This holistic property of compound quantum systems, which invol...