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

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.