How useful is a quantum dynamical operation for quantum information processing? Motivated by this question, we investigate several strength measures quantifying the resources intrinsic to a quantum operation. We develop a general theory of such strength measures, based on axiomatic considerations independent of state-based resources. The power of this theory is demonstrated with applications to quantum communication complexity, quantum computational complexity, and entanglement generation by unitary operations.

We investigate the entanglement characteristics of two general bimodal Bose-Einstein condensates -a pair of tunnel-coupled Bose-Einstein condensates and the atom-molecule Bose-Einstein condensate. We argue that the entanglement is only physically meaningful if the system is viewed as a bipartite system, where the subsystems are the two modes. The indistinguishibility of the particles in the condensate means that the atomic constituents are physically inaccessible and thus the degree of entanglement between individual particles, unlike the entanglement between the modes, is not experimentally relevant so long as the particles remain in the condensed state. We calculate the entanglement between the two modes for the exact ground state of the two bimodal condensates and consider the dynamics of the entanglement in the tunnel-coupled case.

How does the classical phase-space structure for a composite system relate to the entanglement characteristics of the corresponding quantum system? We demonstrate how the entanglement in nonlinear bipartite systems can be associated with a fixed-point bifurcation in the classical dynamics. Using the example of coupled giant spins we show that when a fixed point undergoes a supercritical pitchfork bifurcation, the corresponding quantum state-the ground state-achieves its maximum amount of entanglement near the critical point. We conjecture that this will be a generic feature of systems whose classical limit exhibits such a bifurcation.

We compare and contrast the entanglement in the ground state of two Jahn-Teller models. The E ␤ system models the coupling of a two-level electronic system, or qubit, to a single-oscillator mode, while the E models the qubit coupled to two independent, degenerate oscillator modes. In the absence of a transverse magnetic field applied to the qubit, both systems exhibit a degenerate ground state. Whereas there always exists a completely separable ground state in the E ␤ system, the ground states of the E model always exhibit entanglement. For the E ␤ case we aim to clarify results from previous work, alluding to a link between the ground-state entanglement characteristics and a bifurcation of a fixed point in the classical analog. In the E case we make use of an ansatz for the ground state. We compare this ansatz to exact numerical calculations and use it to investigate how the entanglement is shared between the three system degrees of freedom.