Related papers: Full characterization of modular values for two-di…

The concept of a modular value of an observable of a pre- and post-selected quantum system is introduced. It is similar in form and in some cases has a close connection to the weak value of an observable, but instead of describing an…

Modular values are quantities that described by pre- and postselected states of quantum systems like weak values but are different from them: The associated interaction is not necessary to be weak. We discuss an optimal modular-value-based…

In contrast to that a weak value of an observable is usually divided into real and imaginary parts, here we show that separation into modulus and argument is important for modular values. We first show that modular values are expressed by…

The notion of weak measurement in quantum mechanics has gained a significant and wide interest in realizing apparently counterintuitive quantum effects. In recent times, several theoretical and experimental works have been reported for…

Weak values are usually associated with weak measurements of an observable on a pre- and post-selected ensemble. We show that more generally, weak values are proportional to the correlation between two pointers in a successive measurement.…

We discuss two questions related to the concept of weak values as seen from the standard quantum-mechanics point of view. In the first part of the paper, we describe a scenario where unphysical results similar to those encountered in the…

The products of weak values of quantum observables are shown to be of value in deriving quantum uncertainty and complementarity relations, for both weak and strong measurement statistics. First, a 'product representation formula' allows the…

A precise definition of "weak [quantum] measurements" and "weak value" (of a quantum observable) is offered, and simple finite dimensional examples are given showing that weak values are not unique and therefore probably do not correspond…

We characterize a value of an observable by a `sum rule' for generally non-commuting observables and a `product rule' when restricted to a maximal commuting subalgebra of observables together with the requirement that the value is unity for…

We propose an experimental setup for the implementation of weak measurements in the context of the gedankenexperiment known as Hardy's Paradox. As Aharonov et al. showed, these weak values form a language with which the paradox can be…

Weak measurements have an increasing number of applications in contemporary quantum mechanics. They were originally described as a weak interaction that slightly entangled the translational degrees of freedom of a particle to its spin,…

We refute the widely held belief that the quantum weak value necessarily pertains to weak measurements. To accomplish this, we use the transverse position of a beam as the detector for the conditioned von Neumann measurement of a system…

Recently, weak measurements have attracted a lot of interest as an experimental method for the investigation of non-classical correlations between observables that cannot be measured jointly. Here, I explain how the complex valued…

In the weak measurement formalism of Y. Aharonov et al. the so-called weak value A_w of any observable A is generally a complex number. We derive a physical interpretation of its value in terms of the shift in the measurement pointer's mean…

We develop a formal theory of the weak values with emphasis on the consistency conditions and a probabilistic interpretation in the counter-factual processes. We present the condition for the choice of the post-selected state to give a…

Weak values are the fundamental values for observables in a pre- and post-selected system. Weak values are typically measured by weak measurement, in which weak values appear in the change of not the pre- and post-selected system but the…

A general approach to the measurement of an observable with pre- and post-selection is presented. The limit of weak measurement is studied in detail, and it is shown that the phase of the probe, including a Hamiltonian contribution to it,…

A relation is obtained between weak values of quantum observables and the consistency criterion for histories of quantum events. It is shown that ``strange'' weak values for projection operators (such as values less than zero) always…

In this study we critically examine some important papers on weak measurement and weak values. We find some insufficiency and mistakes in these papers, and we demonstrate that the real parts of weak values provide the back-action to the…

Weak measurements are a new tool for characterizing post-selected quantum systems during their evolution. Weak measurement was originally formulated in terms of von Neumann interactions which are practically available for only the simplest…