Impossibility of Determining the Unknown Quantum Wavefunction of a Single System: Quantum Non-Demolition Measurements, Measurements without Entanglement and Adiabatic Measurements

We establish that the information which can be obtained in the measurement of a single system about the unknown quantum wavefunction of the system is limited to estimates of the expectation values of the measured observables, with the estimate errors satisfying the uncertainty principle. Only the fully apriori known wavefunction could be determined exactly. We consider specifically measurement schemes which may induce minimal change in the measured system, such as quantum non-demolition measurements, measurements without entanglement and adiabatic measurements.