  We review recent experiments on entanglement, Bell's inequality, and
decoherence-free subspaces in a quantum register of trapped \be ions. We have
demonstrated entanglement of up to four ions using the technique of M{\o}lmer
and S{\o}rensen. This method produces the state |down down> + |up up> for two
ions and the state |down down down down> + |up up up up> for four ions. We
generate the entanglement deterministically in each shot of the experiment.
Measurements on the two-ion entangled state violates Bell's inequality at the
$8\sigma$ level. Because of the high detector efficiency of our apparatus, this
experiment closes the detector loophole for Bell's inequality measurements for
the first time. This measurement is also the first violation of Bell's
inequality by massive particles that does not implicitly assume results from
quantum mechanics. Finally, we have demonstrated reversible encoding of an
arbitrary qubit, originally contained in one ion, into a decoherence-free
subspace (DFS) of two ions. The DFS-encoded qubit resists applied collective
dephasing noise and retains coherence under ambient conditions 3.6 times longer
than does an unencoded qubit. The encoding method, which uses single-ion gates
and the two-ion entangling gate, demonstrates all the elements required for
two-qubit universal quantum logic.
