  We study decoherence of one, two, and $n$ non-interacting qubits.
Decoherence, measured in terms of purity, is calculated in linear response
approximation, making use of the spectator configuration. The environment and
its interaction with the qubits are modelled by random matrices. For two
qubits, numerical studies reveal a simple one to one correspondence between its
decoherence and its internal entanglement decay. Using this relation we are
able to give a formula for concurrence decay. For large environments the
evolution induces a unital channel in the two qubits, providing a partial
explanation for the relation above. Using a kicked Ising spin network, we study
the exact evolution of two non-interacting qubits in the presence of a spin
bath. We find that the entanglement (as measured by concurrence) of the two
qubits has a close relation to the purity of the pair, and closely follows an
analytic relation derived for Werner states. As a collateral result we find
that an integrable environment causes quadratic decay of concurrence as well as
of purity, while a chaotic environment causes linear decay. Both quantities
display recurrences in some integrable environments. Good agreement with the
results found using random matrix theory is obtained. Finally, we analyze
decoherence of a quantum register in the absence of non-local operations. The
problem is solved in terms of a sum rule which implies linear scaling in the
number of qubits. Each term involves a single qubit and its entanglement with
the remaining ones. Two conditions are essential: decoherence must be small and
the coupling of different qubits must be uncorrelated in the interaction
picture. We apply the result to the random matrix model, and illustrate its
reach considering a GHZ state coupled to a spin bath.
