  With the recent surge of interest in quantum computation, it has become very
important to develop clear experimental tests for ``quantum behavior'' in a
system. This issue has been addressed in the past in the form of the
inequalities due to Bell and those due to Leggett and Garg. These inequalities
concern the results of ideal projective measurements, however, which are
experimentally difficult to perform in many proposed qubit designs, especially
in many solid state qubit systems. Here, we show that weak continuous
measurements, which are often practical to implement experimentally, can yield
particularly clear signatures of quantum coherence, both in the measured
correlation functions and in the measured power spectrum.
