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Protective measurement of the wave function of a single squeezed harmonic-oscillator state.

The adiabatic ``protective measurement'' suggested by Aharonov, Anandan, and Vaidman [Phys. Lett. A 178, 38 (1993)] is a measurement of a discrete energy eigenstate, in which the entanglement between the measured state and the quantum probe is avoided approximately when they interact adiabatically, and the measured state is left approximately unchanged (up to a phase factor) for all measured observables. This measurement scheme, however, does not overcome the reduction of the measured state, because this state is only approximately, and not exactly, disentangled from the quantum probe. Our recent analysis of a measurement scheme of a squeezed harmonic-oscilllator state [Phys. Rev. A 53, R2911 (1996)], in which the entanglement between the measured state and the probe is avoided exactly, and the measured state is left exactly unchanged (up to a phase factor) for all measured observables, suggests that in order to measure the quantum state of a single system without changing this state, full a priori information about this state is required.