  We study the protective measurement of a qubit by a second qubit acting as a
probe. Consideration of this model is motivated by the possibility of its
experimental implementation in multiqubit systems such as trapped ions. In our
scheme, information about the expectation value of an arbitrary observable of
the system qubit is encoded in the rotation of the state of the probe qubit. We
describe the structure of the Hamiltonian that gives rise to this measurement
and analyze the resulting dynamics under a variety of realistic conditions,
such as noninfinitesimal measurement strengths, repeated measurements,
non-negligible intrinsic dynamics of the probe, and interactions of the system
and probe qubits with an environment. We propose an experimental realization of
our model in an ion trap. The experiment may be performed with existing
technology and makes use of established experimental methods for the
engineering and control of Hamiltonians for quantum gates and quantum
simulations of spin systems.
