Related papers: Weak Value, Quasiprobability and Bohmian Mechanics
In this chapter we offer an introduction to weak values from a three-fold perspective: first, outlining the protocols that enable their experimental determination; next, deriving their correlates in the quantum formalism and, finally,…
We show that the joint behaviour of an arbitrary pair of quantum observables can be described by quasi-probabilities, which are extensions of the standard probabilities used for describing the behaviour of a single observable. The physical…
The concept of a \emph{weak value} of a quantum observable was developed in the late 1980s by Aharonov and colleagues to characterize the value of an observable for a quantum system in the time interval between two projective measurements.…
Bohmian mechanics (BM) is a popular interpretation of quantum mechanics in which particles have real positions. The velocity of a point x in configuration space is defined as the standard probability current j(x) divided by the probability…
In this article, we investigate Bohm's view of quantum theory, especially Bohm's quantum potential, from a new perspective. We develop a quasi-Newtonian approach to Bohmian mechanics. We show that to arrive at Bohmian formulation of quantum…
We present a complex probability measure relevant for double (pairs of) states in quantum mechanics, as an extension of the standard probability measure for single states that underlies Born's statistical rule. When the double states are…
It is shown, that the Aharonov-Albert-Vaidman concept of weak values appears to be a consequence of a more general quantum phenomenon of weak quantum evolution. Here the concept of weak quantum evolution is introduced and discussed for the…
Quasiprobability representations, such as the Wigner function, play an important role in various research areas. The inevitable appearance of negativity in such representations is often regarded as a signature of nonclassicality, which has…
A so called 'weak value' of an observable in quantum mechanics (QM) may be obtained in a weak measurement + post-selection procedure on the QM system under study. Applied to number operators, it has been invoked in revisiting some QM…
Since its introduction 25 years ago, the quantum weak value has gradually transitioned from a theoretical curiosity to a practical laboratory tool. While its utility is apparent in the recent explosion of weak value experiments, its…
Regular quasiprobabilities are introduced for the aim of characterizing quantum correlations of multimode radiation fields. Negativities of these quantum-correlation quasiprobabilities are necessary and sufficient for any quantum…
We propose a general framework of the quantum/quasi-classical transformations by introducing the concept of quasi-joint-spectral distribution (QJSD). Specifically, we show that the QJSDs uniquely yield various pairs of…
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…
Many recent results suggest that quantum theory is about information, and that quantum theory is best understood as arising from principles concerning information and information processing. At the same time, by far the simplest version of…
Non-relativistic quantum mechanics is reformulated here based on the idea that relational properties among quantum systems, instead of the independent properties of a quantum system, are the most fundamental elements to construct quantum…
We explain the properties and clarify the meaning of quantum weak values using only the basic notions of elementary quantum mechanics.
A central feature of quantum mechanics is the non-commutativity of operators used to describe physical observables. In this article, we present a critical analysis on the role of non-commutativity in quantum theory, focusing on its…
This article comprises a review of both the quasi-probability representations of infinite-dimensional quantum theory (including the Wigner function) and the more recently defined quasi-probability representations of finite-dimensional…
Quantum Mechanical weak values are an interference effect measured by the cross-Wigner transform W({\phi},{\psi}) of the post-and preselected states, leading to a complex quasi-distribution {\rho}_{{\phi},{\psi}}(x,p) on phase space. We…
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…