Measurements at the Limit: Are there limits to what can be measured?

Takako Endo, Norio Konno

We investigate "the Wojcik model" introduced and studied by Wojcik et al., which is a one-defect quantum walk (QW) having a single phase at the origin. They reported that giving a phase at one point causes an astonishing effect for localization. There are three types of measures having important roles in the study of QWs: time-averaged limit measure, weak limit measure, and stationary measure. The first two measures imply a coexistence of localized behavior and the ballistic spreading in the QW. As Konno et al. suggested, the time-averaged limit and stationary measures are closely related to each other for some models. In this paper, we focus on a relation between the two measures for the Wojcik model. The stationary measure was already obtained by our previous work. Here, we get the time-averaged limit measure by several methods. Our results show that the stationary measure is a special case of the time-averaged limit measure.

R. Furth

Bernard d’Espagnat

Takako Endo, Norio Konno

We investigate ``the Wojcik model" introduced and studied by Wojcik et al. \cite{wojcik}, which is a one-defect quantum walk (QW) having a single phase at the origin. They reported that giving a phase at one point causes an astonishing effect for localization. Three types of measures have important roles in the study of QWs: time-averaged limit measure, weak limit measure, and stationary measure. The first two measures imply a coexistence of localized behavior and the ballistic spreading in the QW. As Konno et al. \cite{segawa} suggested, the time-averaged limit and stationary measures are closely related to each other for some QWs with one defect. In this paper, we focus on a relation between the two measures for the Wojcik model. The stationary measure was already obtained by our previous work \cite{watanabe}. Here, we get the time-averaged limit measure by several methods. Our results show that the stationary measure is a special case of the time-averaged limit measure.

John Earman, Abner Shimony

Lior Cohen, D. Istrati, Liat Dovrat +1 more

Classically, the resolution of optical measurements is limited by the Rayleigh limit and their sensitivity by the shot noise limit. However, non-classical measurements can surpass these limits. Measuring the photon number parity using a photon-number resolving detector, super resolved phase measurements up to 144 better than the Rayleigh limit are presented, with coherent states of up to 4,200 photons on average. An additional measurement that can be implemented with standard single-photon detectors is proposed and demonstrated. With this scheme, super resolution at the shot noise limit is demonstrated with coherent states of up to 200 photons on average.