We analyze the relationship between tripartite entanglement and genuine tripartite nonlocality for three-qubit pure states in the Greenberger-Horne-Zeilinger class. We consider a family of states known as the generalized Greenberger-Horne-Zeilinger states and derive an analytical expression relating the three-tangle, which quantifies tripartite entanglement, to the Svetlichny inequality, which is a Bell-type inequality that is violated only when all three qubits are nonlocally correlated. We show that states with three-tangle less than 1/2 do not violate the Svetlichny inequality. On the other hand, a set of states known as the maximal slice states does violate the Svetlichny inequality, and exactly analogous to the two-qubit case, the amount of violation is directly related to the degree of tripartite entanglement. We discuss further interesting properties of the generalized Greenberger-Horne-Zeilinger and maximal slice states.

We derive a generalized zero-range pseudopotential applicable to all partial wave solutions to the Schrödinger equation based on a delta-shell potential in the limit that the shell radius approaches zero. This properly models all higher order multipole moments not accounted for with a monopolar delta function at the origin, as used in the familiar Fermi pseudopotential for s-wave scattering. By making the strength of the potential energy dependent, we derive self-consistent solutions for the entire energy spectrum of the realistic potential. We apply this to study two particles in an isotropic harmonic trap, interacting through a central potential, and derive analytic expressions for the energy eigenstates and eigenvalues.

We analyze the interplay of chaos, entanglement, and decoherence in a system of qubits whose collective behavior is that of a quantum kicked top. The dynamical entanglement between a single qubit and the rest can be calculated from the mean of the collective spin operators. This allows the possibility of efficiently measuring entanglement dynamics in an experimental setting. We consider a deeply quantum regime and show that signatures of chaos are present in the dynamical entanglement for parameters accessible in an experiment that we propose using cold atoms. The evolution of the entanglement depends on the support of the initial state on regular versus chaotic Floquet eigenstates, whose phase-space distributions are concentrated on the corresponding regular or chaotic eigenstructures. We include the effect of decoherence via a realistic model and show that the signatures of chaos in the entanglement dynamics persist in the presence of decoherence. In addition, the classical chaos affects the decoherence rate itself.

We investigate controlled collisions between trapped but separated ultracold atoms. The interaction between atoms is treated self-consistently using an energy-dependent delta-function pseudopotential model, whose validity we establish. At a critical separation, a "trap-induced shape resonance" between a molecular bound states and a vibrational eigenstate of the trap can occur. This resonance leads to an avoided crossing in the eigenspectrum as a function of separation. We investigate how this new resonance can be employed for quantum control. The ability to arbitrarily manipulate the quantum state of a many-body ensemble represents the ultimate control of a physical system. This task has steadily advanced in atomic-molecular-optical systems with tremendous progress in cooling and trapping technology. This has led to the creation of Bose-Einstein condensates (BEC) and Fermi degenerate gases, and the explorations of new forms of matter and mesoscopic quantum states previously accessible only in condensed matter systems The standard approach to modelling and designing coherent states of matter, such as occur in a quantum phase transition, has its foundations in condensed matter theory, where one considers solutions to the entire manybody Hamiltonian. An alternative viewpoint arises from a fundamental theorem of quantum information theory [6]: an arbitrary state of a many-body system can be reached entirely through operations on single bodies and pairwise interactions. This provides a direct approach to engineering mesoscopic states through the application of a "quantum circuit" [7]. Moreover, one requires only a single two-body interaction (e.g. CPHASE or CNOT gate) that entangles the "particles" to contribute to a universal set of quantum logic gates.In the context of ultracold neutral atoms, whereas manipulating the quantum state of an individual atom is a very mature technique, arbitrary unitary mapping of a two-atom system has not yet been achieved. Neutrals, by their very nature, do not strongly couple to anything. This may be an advantage for avoiding noise, but it implies that the two-body interaction will generally require close overlap of the atomic wavepackets.By bringing two atoms within the same well of a tightly confining microtrap, one can achieve this strong coupling while remaining in the electronic ground state. Proposals for two-atom control in such a geometry have been considered using ground state s-wave collisions [8], Feshbach resonances [9] and laser induced Raman transitions [10]. At such close range, the atoms lose their individual identities and instead must be described as a molecular dimer which generally does not respect the atomic symmetries. This constrains the possible encodings of quantum information such that two-body logic gates can be performed within a well-defined "logical basis". This constraint can be overcome by placing the particles in distinguishable locations where the atomic quantum numbers are conserved asymptotically. Under typical conditions such separated atoms would...

We describe a scalable, high-speed, and robust architecture for measurement-based quantum computing with trapped ions. Measurement-based architectures offer a way to speed up operation of a quantum computer significantly by parallelizing the slow entangling operations and transferring the speed requirement to fast measurement of qubits. We show that a 3D cluster state suitable for fault-tolerant measurement-based quantum computing can be implemented on a 2D array of ion traps. We propose the projective measurement of ions via multiphoton photoionization for nanosecond operation and discuss the viability of such a scheme for Ca ions.