Radu Ionicioiu

Mesoscopic Stern-Gerlach device to polarize spin currents

Spin preparation and spin detection are fundamental problems in spintronics and in several solid-state proposals for quantum information processing. Here we propose the mesoscopic equivalent of an optical polarizing beam splitter. This interferometric device uses nondispersive phases (Aharonov-Bohm and Rashba) in order to separate spin-up and spin-down carriers into distinct outputs and thus it is analogous to a Stern-Gerlach apparatus. It can be used both as a spin preparation device and as a spin measuring device by converting spin into charge (orbital) degrees of freedom. An important feature of the proposed spin polarizer is that no ferromagnetic contacts are used.

Ground state entanglement and geometric entropy in the Kitaev model

We study the entanglement properties of the ground state in Kitaevs model. This is a two-dimensional spin system with a torus topology and nontrivial four-body interactions between its spins. For a generic partition

Bipartite entanglement and entropic boundary law in lattice spin systems

(A,B)

Quantum fidelity and quantum phase transitions in matrix product states

of the lattice we calculate analytically the von Neumann entropy of the reduced density matrix

QUANTUM COMPUTATION WITH BALLISTIC ELECTRONS

\rho_A

Testing Bell’s inequality with ballistic electrons in semiconductors

in the ground state. We prove that the geometric entropy associated with a region

Entangling spins by measuring charge: A parity-gate toolbox

A

Generalized Toffoli gates using qudit catalysis

is linear in the length of its boundary. Moreover, we argue that entanglement can probe the topology of the system and reveal topological order. Finally, no partition has zero entanglement and we find the partition that maximizes the entanglement in the given ground state.

Quantum gates with topological phases

We investigate bipartite entanglement in spin-1/2 systems on a generic lattice. For states that are an equal superposition of elements of a group G of spin flips acting on the fully polarized state |0>{sup xn}, we find that the von Neumann entropy depends only on the boundary between the two subsystems A and B. These states are stabilized by the group G. A physical realization of such states is given by the ground state manifold of the Kitaevs model on a Riemann surface of genus g. For a square lattice, we find that the entropy of entanglement is bounded from above and below by functions linear in the perimeter of the subsystem A and is equal to the perimeter (up to an additive constant) when A is convex. The entropy of entanglement is shown to be related to the topological order of this model. Finally, we find that some of the ground states are absolutely entangled, i.e., no partition has zero entanglement. We also provide several examples for the square lattice.

Quantum-information processing in bosonic lattices

Matrix product states, a key ingredient of numerical algorithms widely employed in the simulation of quantum spin chains, provide an intriguing tool for quantum phase transition engineering. At critical values of the control parameters on which their constituent matrices depend, singularities in the expectation values of certain observables can appear, in spite of the analyticity of the ground state energy. For this class of generalized quantum phase transitions, we test the validity of the recently introduced fidelity approach, where the overlap modulus of ground states corresponding to slightly different parameters is considered. We discuss several examples, successfully identifying all the present transitions. We also study the finite size scaling of fidelity derivatives, pointing out its relevance in extracting critical exponents.