  We show that when a suitable entanglement generating unitary operator
depending on a parameter is applied on N qubits in parallel, and an appropriate
observable is measured, a precision of order 2 raised to the power (-N) in
estimating the parameter may be achieved. This exponentially improves the
precision achievable in classical and in quantum non-entangling parallel
strategies. We propose a quantum-optics model of laser light interacting with
an N-qubit system, say a polyatomic molecule, via a generalized Jaynes-Cummings
interaction which, in principle, could achieve the exponentially enhanced
precision.
