Various embodiments of the present invention are directed to methods for determining a phase shift acquired by an entangled N-qubit system represented by a NOON state. In one embodiment, a probe electromagnetic field is coupled with each qubit system. The phase shift acquired by the qubit systems is transferred to the probe electromagnetic field by transforming each qubit-system state into a linear superposition of qubit basis states. An intensity measurement is performed on the probe electromagnetic field in order to obtain a corresponding measurement result. A counter associated with a measurement-result interval is incremented, based on the measurement result falling within the measurement-result interval. A frequency distribution is produced by normalizing the counter associated with each measurement-result interval for a number of trials. The phase shift is determined by fitting a probability distribution associated with the probe electromagnetic field to the frequency distribution as a function of the phase shift.