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Three qubits can be entangled in two inequivalent ways
Invertible local transformations of a multipartite system are used to define equivalence classes in the set of entangled states. This classification concerns the entanglement properties of a singleExpand
Long-distance quantum communication with atomic ensembles and linear optics
It is shown that the communication efficiency scales polynomially with the channel length, and hence the scheme should be operable over very long distances. Expand
Cold Bosonic Atoms in Optical Lattices
The dynamics of an ultracold dilute gas of bosonic atoms in an optical lattice can be described by a Bose-Hubbard model where the system parameters are controlled by laser light. We study theExpand
Matrix product state representations
The freedom in representations with and without translation symmetry are determined, derive respective canonical forms and provide efficient methods for obtaining them. Expand
Quantum Repeaters: The Role of Imperfect Local Operations in Quantum Communication
This work presents a scheme of a quantum repeater that connects a string of (imperfect) entangled pairs of particles by using a novel nested purification protocol, thereby creating a single distant pair of high fidelity. Expand
Matrix product states, projected entangled pair states, and variational renormalization group methods for quantum spin systems
This article reviews recent developments in the theoretical understanding and the numerical implementation of variational renormalization group methods using matrix product states and projectedExpand
Renormalization algorithms for Quantum-Many Body Systems in two and higher dimensions
We describe quantum many--body systems in terms of projected entangled--pair states, which naturally extend matrix product states to two and more dimensions. We present an algorithm to determineExpand
Quantum State Transfer and Entanglement Distribution among Distant Nodes in a Quantum Network
We propose a scheme to utilize photons for ideal quantum transmission between atoms located at spatially separated nodes of a quantum network. The transmission protocol employs special laser pulsesExpand
Optimization of entanglement witnesses
An entanglement witness (EW) is an operator that allows to detect entangled states. We give necessary and sufficient conditions for such operators to be optimal, i.e. to detect entangled states in anExpand
Dipole blockade and quantum information processing in mesoscopic atomic ensembles.
A technique for manipulating quantum information stored in collective states of mesoscopic ensembles by optical excitation into states with strong dipole-dipole interactions that can be employed for controlled generation of collective atomic spin states as well as nonclassical photonic states and for scalable quantum logic gates is described. Expand