Pre- and post-selection, weak values and contextuality

Abstract

By analyzing the concept of contextuality (Bell-Kochen-Specker) in terms of pre-and-post-selection (PPS), it is possible to assign definite values to observables in a new and surprising way. Physical reasons are presented for restrictions on these assignments. When measurements are performed which do not disturb the pre-and post-selection (i.e. weak measurements), then novel experimental aspects of contextuality can be demonstrated including a proof that every PPS-paradox with definite predictions implies contextuality. Certain results of these measurements (eccentric weak values with e.g. negative values outside the spectrum), however, cannot be explained by a "classicallike" hidden variable theory.

On the role of complex phases in the quantum statistics of weak measurements

“…In particular, weak conditional probabilities provide an empirical tool for the investigation of non-classical correlations between measurement results that cannot be obtained jointly. As shown in a number of recent experiments [5,[7][8][9][10][11][12][13][14][15][16], it is then possible to explain quantum paradoxes in terms of negative conditional probabilities for the weakly measured alternatives m. In such demonstrations of non-classical statistics, weak conditional probabilities establish a link between the conventional representation of quantum coherence as a wave-like property and classical probability theory. Equation (8) expresses this fundamental relation between the complex conditional probabilities obtained in weak measurements and the quantum coherence of Hilbert space.…”

Measuring which-path information with coupled electronic Mach-Zehnder interferometers

“…35,56,[72][73][74] The paper is organized as follows. In Section II, we describe the considered geometry and our physical modeling principles before reviewing and applying the scattering theory of mesoscopic transport to the two edge state physics.…”

Quantum key distribution using sequential weak values

“…From this we can see that the probability of the state being unchanged after the weak measurement interaction is [26] …”

“…Weak measurements can be described using the general von Neumann model of quantum measurement [10,11,26]. Consider an observable A pertaining to a quantum system pre-selected to be in the state |ψ in .…”

“…To see the sense in which the measurement can be said to yield "information without disturbance" in the limit of vanishing g, consider the following: first, we note the important result that [12,26] …”