Saturating a Fundamental Bound of Quantum Measurements Accuracy

A quantum observable is typically measured by relating it, through interactions, to the observable of a second quantum system, or meter. In this scenario, fundamental limitations arise as stated by the celebrated Wigner-Araki-Yanase theorem and its generalizations predicting an upper-bound on the measurement’s accuracy. Is it possible to saturate this fundamental bound? Here, we propose a simple interferometric setup, arguably within reach of present technology, in which a flying particle (the quantum meter) is used to measure the state of a qubit (the target system). We show that the bound can be saturated and that this happens only if the flying particle is prepared in a Gaussian wavepacket.