Related papers: Three results on weak measurements

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…

It is well known that any projective measurement can be decomposed into a sequence of weak measurements, which cause only small changes to the state. Similar constructions for generalized measurements, however, have relied on the use of an…

We present ten different characterizations of functions satisfying a weak reverse H\"older inequality on an open subset of a metric measure space with a doubling measure. Among others, we describe these functions as a class of weak…

This paper establishes new common fixed point theorems for weakly compatible mappings in metric spaces, relaxing traditional requirements such as continuity, compatibility, and reciprocal continuity. We present a unified framework for three…

A statistical analysis of optimal universal cloning shows that it is possible to identify an ideal (but non-positive) copying process that faithfully maps all properties of the original Hilbert space onto two separate quantum systems. The…

We describe space--time fluctuations by means of small fluctuations of the metric on a given background metric. From a minimally coupled Klein--Gordon equation we obtain within a weak-field approximation up to second order and an averaging…

Weak measurement is unique in enabling measurements of non-commuting operators as well as otherwise-undetectable peculiar phenomena predicted by the Two-State-Vector-Formalism (TSVF). This article, the first in two parts, explores novel…

Weak measurement has been shown to play important roles in the investigation of both fundamental and practical problems. Anomalous weak values are generally believed to be observed only when post-selection is performed, i.e, only a…

Quantum mechanics does not permit joint measurements of non-commuting observables. However, it is possible to measure the weak value of a projection operator, followed by the precise measurement of a different property. The results can be…

We study the effect of decoherence on a weak value measurement in a paradigm system consisting of a double quantum dot continuously measured by a quantum point contact. Fluctuations of the parameters controlling the dot state induce…

We derive schemes to measure the so-called weak values of quantum system observables by coupling of the system to a qubit meter system. We highlight, in particular, the meaning of the imaginary part of the weak values, and show how it can…

It is argued that a weak value of an observable is a robust property of a single pre- and post-selected quantum system rather than a statistical property. During an infinitesimal time a system with a given weak value affects other systems…

We show that in wavepacket tunnelling localisation of the transmitted particle amounts to a quantum measurement of the delay it experiences in the barrier. With no external degree of freedom involved, the envelope of the wavepacket plays…

Weak measurements in combination with post-selection can give rise to a striking amplification effect (related to a large "weak value"). We show that this effect can be understood by viewing the initial state of the pointer as the ground…

We discuss the abstract structure of sequential weak measurement (WM) of general observables. In all orders, the sequential WM correlations without post-selection yield the corresponding correlations of the Wigner function, offering direct…

Weak amplification is a signal enhancement technique which is used to measure tiny changes that otherwise cannot be determined because of technical limitations. It is based on the existence of a special type of interaction which couples a…

In the cited paper [White, T., Mutus, J., Dressel, J. et al., "Preserving entanglement during weak measurement demonstrated with a violation of the Bell-Leggett-Garg inequality", npj Quantum Information 2, 15022 (2016), arXiv:1504.02707],…

We establish a framework for the study of the effective theory of weak convergence of measures. We define two effective notions of weak convergence of measures on $\mathbb{R}$: one uniform and one non-uniform. We show that these notions are…

Let (X,dX) and (Y,dY) be semimetric spaces with distance sets D(X) and, respectively, D(Y). A mapping F : X \to Y is a weak similarity if it is surjective and there exists a strictly increasing f : D(Y) \to D(X) such that dX = f \circ dY…

A while loop tests a termination condition on every iteration. On a quantum computer, such measurements perturb the evolution of the algorithm. We define a while loop primitive using weak measurements, offering a trade-off between the…