Related papers: The Reconstruction Problem and Weak Quantum Values
We generalize the concept of a weak value of a quantum observable to cover arbitrary real positive operator measures. We show that the definition is operationally meaningful in the sense that it can be understood within the quantum theory…
We study the weak values of a quantum observable from the point of view of the Wigner formalism. The main actor is here the cross-Wigner transform of two functions, which is in disguise the cross-ambiguity function familiar from radar…
Weak values are average quantities,therefore investigating their associated variance is crucial in understanding their place in quantum mechanics. We develop the concept of a position-postselected weak variance of momentum as cohesively as…
We investigate the sequential composition of weak values in the framework of time-symmetric quantum mechanics. Specifically, we consider a forward'' weak measurement from a preselected state $\ket{\psi}$ to a post-selected state…
We re-examine the status of the weak value of a quantum mechanical observable as an objective physical concept, addressing its physical interpretation and general domain of applicability. We show that the weak value can be regarded as a…
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,…
Weak measurement of a quantum system followed by postselection based on a subsequent strong measurement gives rise to a quantity called the weak value: a complex number for which the interpretation has long been debated. We analyse the…
Conventional quantum mechanics describes a pre- and post-selected system in terms of virtual (Feynman) paths via which the final state can be reached. In the absence of probabilities, a weak measurement (WM) determines the probability…
The quantum mechanical weak value $A_w=\left\langle \phi|A|\psi \right \rangle / \left\langle \phi | \psi \right\rangle$ of an observable $A$ is a measurable quantity associated with an observable $A$ and pre- and post-selected states…
We investigate four key issues with using a nonzero weak value of the spatial projection operator to infer the past path of an individual quantum particle. First, we note that weak measurements disturb a system, so any approach relying on…
Weak values have been shown to be helpful especially when considering them as the outcomes of weak measurements. In this paper we show that in principle, the real and imaginary parts of the weak value of any operator may be elucidated from…
The weak value of an observable is experimentally accessible by weak measurements as theoretically analyzed by Aharonov et al. and recently experimentally demonstrated. We introduce a weak operator associated with the weak values and give a…
A quantum transition can be seen as a result of interference between various pathways(e.g. Feynman paths) which can be labelled by a variable $f$. An attempt to determine the value of f without destroying the coherence between the pathways…
In quantum theory, a weak value is a complex number with a somewhat technical definition: it is a ratio whose numerator is the matrix element of a self-adjoint operator and whose denominator is the inner product of a corresponding pair of…
The real part of the weak value is identified as the conditional Bayes probability through the quantum analog of the Bayes relation. We present an explicit protocol to get the the weak values in a simple Mach-Zehnder interferometer model…
We present an analysis of a double Mach-Zehnder interferometer in which an ensemble of identical pre- and postselected particles leave a weak trace. A knowledge of the weak value partially destroys the quantum interference. The results,…
Quantum resonance, i.e., amplification in transition probability available under certain conditions, offers a powerful means for determining fundamental quantities in physics, including the time duration of the second adopted in the SI…
Weak measurement is a standard measuring procedure with two changes: it is performed on pre- and post-selected quantum systems and the coupling to the measuring device is weakened. The outcomes of weak measurements, ``weak values'' are very…
We address the issue of how to properly treat, and in a more general setting, the concept of a weak value of a weak measurement in quantum mechanics. We show that for this purpose, one must take in account the effects of the measuring…
A quantum state contains the maximal amount of information available for a given quantum system. In this paper we use weak-value expressions to reconstruct quantum states of continuous-variable systems in the quantum optical domain. The…