Instability and entanglement of the ground state of the Dicke model.

Using tools of quantum information theory we show that the ground state of the Dicke model exhibits an infinite sequence of instabilities (quantum-phase-like transitions). These transitions are characterized by abrupt changes of the bi-partite entanglement between atoms at critical values kappa(j) of the atom-field coupling parameter kappa and are accompanied by discontinuities of the first derivative of the energy of the ground state. We show that in a weak-coupling limit (kappa1 < or = kappa < or = kappa2) the Coffman-Kundu-Wootters inequalities are saturated, which proves that for these values of the coupling no intrinsic multipartite entanglement (neither among the atoms nor between the atoms and the field) is generated by the atom-field interaction.

Experimental realization of the quantum universal NOT gate.

In classical computation, a 'bit' of information can be flipped (that is, changed in value from zero to one and vice versa) using a logical NOT gate; but the quantum analogue of this process is much more complicated. A quantum bit (qubit) can exist simultaneously in a superposition of two logical states with complex amplitudes, and it is impossible to find a universal transformation that would flip the original superposed state into a perpendicular state for all values of the amplitudes. But although perfect flipping of a qubit prepared in an arbitrary state (a universal NOT operation) is prohibited by the rules of quantum mechanics, there exists an optimal approximation to this procedure.

Thermalizing quantum machines: dissipation and entanglement.

We study the relaxation of a quantum system towards the thermal equilibrium using tools developed within the context of quantum information theory. We consider a model in which the system is a qubit, and reaches equilibrium after several successive two-qubit interactions (thermalizing machines) with qubits of a reservoir. We characterize completely the family of thermalizing machines.

No-signaling condition and quantum dynamics.

We show that the basic dynamical rules of quantum physics can be derived from its static properties and the condition that superluminal communication is forbidden. More precisely, the fact that the dynamics has to be described by linear completely positive maps on density matrices is derived from the following assumptions: (1) physical states are described by rays in a Hilbert space, (2) probabilities for measurement outcomes at any given time are calculated according to the usual trace rule, and (3) superluminal communication is excluded. This result also constrains possible nonlinear modifications of quantum physics.