Weak Value and Weak Measurements

Miguel Orszag

Kazuhisa Ogawa, Osamu Yasuhiko, Hirokazu Kobayashi +2 more

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 value 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.

Lev Vaidman A

Stephen Parrott

Precise definitions of "weak [quantum] measurements" and "weak value" [of a quantum observable] are offered, which seem to capture the meaning of the often vague ways that these terms are used in the literature. Simple finite dimensional examples are given showing that weak values of an observable are not unique, and in fact arbitrary weak values can be obtained by appropriate weak measurements. This implies that a "weak value" of an observable A, *by itself*, can furnish no unambiguous information about A; any information in a weak value is inextricably connected with the particular measurement procedure used to obtain that weak value. Moreover, arbitrary weak values can be obtained using a "meter space" of dimension as small as 2. A "Remarks" section questions the utility of "weak measurement".

Enrico Rebufello, Fabrizio Piacentini, Alessio Avella +7 more

Despite being very influential on both foundations and applications of quantum mechanics, weak values are still somewhat controversial. Although there are some indications that weak values are physical properties of a single quantum system, the common way weak values are presented is statistical: it is commonly believed that for measuring weak values one has to perform many weak measurements over a large ensemble of pre- and postselected particles. Other debates surround the anomalous nature of weak value and even their quantumness. To address these issues, we present some preliminary data showing that anomalous weak values can be measured using just a single detection, i.e. with no statistics. In our experiment, a single click of a detector indicates the weak value as a single photon property, which moreover lies well beyond the range of eigenvelues of the measured operator. Importantly, the uncertainty with which the weak values is measured is smaller than the difference between the weak value and the closet eigenvalue. This is the first experimental realization of robust weak measurements.

Prashanna Simkhada, Jean-François S. Van Huele