Abstract

It has been shown by Aharanov el al.¹ that the inner product of two quantum states can be interpreted as a measure of the proximity of these two states in phase space. In a related interpretation, Wódkiewicz² suggested an 'operational approach' to phase space measurements, in which the projection of the state of the system onto a reference state, denoted a “quantum ruler” state in some prepared measurement basis, with its associated localisation in phase space, is seen as an attempt to measure simultaneously both the canonical position and momentum. For example, if our measurement involves the projection of the system onto a coherent state, then after the measurement we have gained simultaneous information concerning the position and momentum of the system located to within the quantum ruler coherent state phase space error circle.

© 1996 IEEE