26pRF-3 Optimal Covariant Measurement of Momentum on a Half Line in Qunatum Mechanics

Yutaka Shikano, 暁夫 細谷

Yutaka Shikano, Akio Hosoya

We cannot perform the projective measurement of a momentum on a half line since it is not an observable. Nevertheless, we would like to obtain some physical information of the momentum on a half line. We define an optimality for measurement as minimizing the variance between an inferred outcome of the measured system before a measuring process and a measurement outcome of the probe system after the measuring process, restricting our attention to the covariant measurement studied by Holevo [Rep. Math. Phys. 13, 379 (1978)]. Extending the domain of the momentum operator on a half line by introducing a two dimensional Hilbert space to be tensored, we make it self-adjoint and explicitly construct a model Hamiltonian for the measured and probe systems. By taking the partial trace over the newly introduced Hilbert space, the optimal covariant positive operator valued measure of a momentum on a half line is reproduced. We physically describe the measuring process to optimally evaluate the momentum of a particle on a half line.

Yutaka Shikano, Akio Hosoya

We cannot perform the projective measurement of a momentum on a half line since it is not an observable.Nevertheless, we would like to obtain some physical information of the momentum on a half line.We define an optimality for mea- surement as minimizing the variance between an inferred outcome of the measured system before a measuring process and a measurement outcome of the probe system after the measuring process, restricting our attention to the covariant measurement studied by Holevo.Extending the domain of the momentum operator on a half line by introducing a two dimensional Hilbert space to be tensored, we make it self- adjoint and explicitly construct a model Hamiltonian for the measured and probe systems.By taking the partial trace over the newly introduced Hilbert space, the optimal covariant positive operator valued measure (POVM) of a momentum on a half line is reproduced.We physically describe the measuring process to optimally evaluate the momentum of a particle on a half line.

Teiko Heinonen

Yutaka Shikano, Akio Hosoya, Alexander I. Lvovsky

We investigate an optimal covariant measurement to measure a momentum of a particle. Given an instantaneous interaction and an infinite measurement time, we explicitly construct a measurement model to satisfy the optimal covariant positive operator valued measure by Holevo and physically consider this measurement model. Furthermore, we apply this model to measure a momentum of a particle on a half line.

D. M. Appleby