Impossibility of determining the quantum wavefunction of a single system and fundamental limit to external force detection

Technology has advanced to the point that single quantum systems can now be controlled. Due to these advances, open fundamental questions in quantum theory are now being faced in laboratories. The possibility of performing a series of measurements on a single quantum system has renewed interest in the question of the physical reality of the wavefunction: What is the limit to the determination of the quantum wavefunction of a single system? It was suggested recently that it may be possible to determine the unknown quantum wavefunction of a single system. State-of-the-art precision measurements, which are based on the monitoring of the time evolution of a single physical system, have renewed interest in the question of the quantum Zeno effect of a single system, and that of the fundamental quantum limit to precision measurements: What is the limit to the determination of the time evolution of a single system and the external classical potentials which shape this time evolution? It was suggested that there may be no such limit. This dissertation establishes the quantum theoretical limits to the information which can be obtained in the measurement of a single system. We prove that information about the unknown quantum wavefunction of the system is limited to estimates of the expectation values of the measured observables, where the estimate errors satisfy the uncertainty principle. This is due to the reduction: In a series of measurements of a single system, each measurement changes the wavefunction of the measured system in accordance with the measurement result, and therefore the statistics of each measurement result depend on the results of all previous measurements. The quantum measurement which does not change the wavefunction of the measured system at all requires full a-priori knowledge of this wavefunction. We prove that this impossibility of determining the quantum wavefunction of a single system and the quantum Zeno effect of a single system are equivalent, and impose a fundamental quantum limit to external force detection. In the monitoring of a single harmonic oscillator, this limit requires an exchange of at least one quantum of energy between the force and the oscillator.