  We study the problem of environmentally-induced decoherence in a
near-critical one-dimensional system of N>>1 coupled qubits. Using the
Jordan-Wigner fermion representation of the qubit operators we identify the
decoherence rates relevant for the two-qubit reduced density matrix. We find
that a desirable onset of massive shared entanglement in the near-critical
regime comes at the expense of decoherence which also tends to increase as the
system is tuned towards criticality. Our results reveal rather contradictory
general requirements that future designs of a qubit chain-based quantum
information processor will need to satisfy.
