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A one-dimensional quantum oscillator is monitored by taking repeated positionmeasurements. As a first con- tribution, it is shown that, under a quantumnondemolition measurement scheme applied to a system initially at the groundstate, (i) the observed sequence of measurements (quantum tracks) correspondingto a single experiment converges to a limit point, and that (ii) the limitpoint is random over the ensemble of the experiments, being distributed as azero-mean Gaussian random variable with a variance at most equal to theground-state variance. As a second contribution, the richer scenario where theoscillator is coupled with a frozen (i.e., at the ground state) ensemble ofindependent quantum oscillators is considered. A sharply different behavioremerges: under the same measurement scheme, here we observe that themeasurement sequences are essentially divergent. Such a rigorous statisticalanalysis of the sequential measurement process might be useful forcharacterizing the main quantities that are currently used for inference,manipulation, and monitoring of many quantum systems. Several interestingproperties of the quantum tracks evolution, as well as of the associated(quantum) threshold crossing times, are discussed and the dependence upon themain system parameters (e.g., the choice of the measurement sampling time, thedegree of interaction with the environment, the measurement device accuracy) iselucidated. At a more fundamental level, it is seen that, as an application ofbasic quantum mechanics principles, a sharp difference exists between theintrinsic randomness unavoidably present in any quantum system, and theextrinsic randomness arising from the environmental coupling, i.e., therandomness induced by an external source of disturbance.

Sequential nonideal measurements of quantum oscillators: Statistical characterization with and without environmental coupling