A framework for measuring weak values without weak interactions and its diagrammatic representation

TL;DR

This paper introduces a unified framework and diagrammatic tool for measuring weak values without relying on weak system-probe interactions, enabling more efficient and versatile measurement techniques.

Contribution

A novel framework using probe-controlled system transformations replaces weak interactions, enhancing understanding and enabling new measurement methods for weak values.

Findings

Developed a diagrammatic representation for the framework

Derived a new, more efficient wavefunction measurement method

Unified various weak measurement techniques under one framework

Abstract

Weak values are typically obtained experimentally by performing weak measurements, which involve weak interactions between the measured system and a probe. However, the determination of weak values does not necessarily require weak measurements, and several methods without weak system-probe interactions have been developed previously. In this work, a framework for measuring weak values is proposed to describe the relationship between various weak measurement techniques in a unified manner. This framework, which uses a probe-controlled system transformation instead of the weak system-probe interaction, improves the understanding of the currently used weak value measurement methods. Furthermore, a diagrammatic representation of the proposed framework is introduced to intuitively identify the complex values obtained in each measurement system. By using this diagram, a new method for measuring weak values with a desired function can be systematically derived. As an example, a scan-free and more efficient direct measurement method of wavefunctions than the conventional techniques using weak measurements is developed.