Entanglement distillation by dissipation and continuous quantum repeaters.

Even though entanglement is very vulnerable to interactions with the environment, it can be created by purely dissipative processes. Yet, the attainable degree of entanglement is profoundly limited in the presence of noise sources. We show that distillation can also be realized dissipatively, such that a highly entangled steady state is obtained.

Quantum Metropolis sampling.

The original motivation to build a quantum computer came from Feynman, who imagined a machine capable of simulating generic quantum mechanical systems--a task that is believed to be intractable for classical computers. Such a machine could have far-reaching applications in the simulation of many-body quantum physics in condensed-matter, chemical and high-energy systems. Part of Feynman's challenge was met by Lloyd, who showed how to approximately decompose the time evolution operator of interacting quantum particles into a short sequence of elementary gates, suitable for operation on a quantum computer.

Quantum simulators, continuous-time automata, and translationally invariant systems.

The general problem of finding the ground state energy of lattice Hamiltonians is known to be very hard, even for a quantum computer. We show here that this is the case even for translationally invariant systems in 1D. We also show that a quantum computer can be built in a 1D chain with a fixed, translationally invariant Hamitonian consisting of nearest-neighbor interactions only.

Delocalized entanglement of atoms in optical lattices.

We show how to detect and quantify entanglement of atoms in optical lattices in terms of correlation functions of the momentum distribution. These distributions can be measured directly in the experiments. We introduce two kinds of entanglement measures related to the position and the spin of the atoms.

Ensemble quantum computation with atoms in periodic potentials.

We show how to perform universal quantum computation with atoms confined in optical lattices which works both in the presence of defects and without individual addressing. The method is based on using the defects in the lattice, wherever they are, both to "mark" different copies on which ensemble quantum computation is carried out and to define pointer atoms which perform the quantum gates. We also show how to overcome the problem of scalability in this system.