Related papers: Uncertainty relations for time averaged weak value…

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…

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…

The notion of trajectory of an individual particle is strictly inhibited in quantum mechanics because of the uncertainty principle. Nonetheless, the weak value, which has been proposed as a novel and measurable quantity definable to any…

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…

We investigate the estimation of a small interaction parameter from the outcomes of weak quantum measurements implemented by the interaction. The relation of weak values and sensitivity is explained and the different contributions of…

We analyze the average of weak values over statistical ensembles of pre- and post-selected states. The protocol of weak values, proposed by Aharonov et al., is the result of a weak measurement conditional on the outcome of a subsequent…

Although time measurements are routinely performed in laboratories, their theoretical description is still an open problem. Correspondingly, the status of the energy-time uncertainty relation is unsettled. In the first part of this work the…

The article recapitulates the concept of weak measurement in its broader sense encapsulating the trade between asymptotically weak measurement precision and asymptotically large measurement statistics. Essential applications in…

Following to the Weil method we generalize the Heisenberg-Robertson uncertainty relation for arbitrary two operators. Consideration is made in spherical coordinates, where the distant variable is restricted from one side, . By this reason…

In this article we continue the study of the quenched distributions of transient, one-dimensional random walks in a random environment. In a previous article we showed that while the quenched distributions of the hitting times do not…

We explore further the suggestion to describe a pre- and post-selected system by a two-state, which is determined by two conditions. Starting with a formal definition of a two-state Hilbert space and basic operations, we systematically…

Energy-time uncertainty plays an important role in quantum foundations and technologies, and it was even discussed by the founders of quantum mechanics. However, standard approaches (e.g., Robertson's uncertainty relation) do not apply to…

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…

A weak measurement performed on a pre- and post-selected quantum system can result in an average value that lies outside of the observable's spectrum. This effect, usually referred to as an "anomalous weak value", is generally believed to…

We study inelastic resonant scattering of a Gaussian wave packet with the parameters close to a zero of the complex scattering coefficient. We demonstrate, both theoretically and experimentally, that such near-zero scattering can result in…

The result of a physical measurement depends on the timescale of the experimental probe. In solid-state systems, this simple quantum mechanical principle has far-reaching consequences: the interplay of several degrees of freedom close to…

We analyze the weak and critical points of various uncertainty relations that follow from the inequalities for the norms of vectors in the Hilbert space of states of a quantum system. There are studied uncertainty relations for sums of…

The canonical commutation relation is the hallmark of quantum theory and Heisenberg's uncertainty relation is a direct consequence of it. But despite its fundamental role in quantum theory, surprisingly, its genuine direct experimental test…

This work considers uncertainty relations on time frequency distributions from a signal processing viewpoint. An uncertainty relation on the marginalizable time frequency distributions is given. A result from quantum mechanics is used on…

We compare the sensitivity of a recent bound on time variation of the fine structure constant from optical clocks with bounds on time varying fundamental constants from atomic clocks sensitive to the electron-to-proton mass ratio, from…