Related papers: Reconstructing weak values without weak measuremen…

We study the detection capability of the weak-value amplification on the basis of the statistical hypothesis testing. We propose a reasonable testing method in the physical and statistical senses to find that the weak measurement with the…

The main purpose of this short article is to give a brief overview of the development of the very interesting weak measurement protocol. I add some comments relating to the reality of weak values, and also comment on the allowed values of…

We present a novel method for reconstructing the shape of an object from measured gradient data. A certain class of optical sensors does not measure the shape of an object, but its local slope. These sensors display several advantages,…

The variance of an observable in a pre-selected quantum system, which is always real and non-negative, appears as an increase in the probe wave packet width in indirect measurements. Extending this framework to pre- and post-selected…

In the weak measurement (WM) scenario involving weak interaction and postselection by projective measurement, the empirical significance of weak values is manifested in terms of shifts in the measurement pointer's mean position and mean…

High resolution reconstruction of complicated objects from incomplete and noisy data can be achieved by solving modulation equations iteratively under physical constraints. This direct demodulation method is a powerful technique for dealing…

An interferometric arrangement is proposed in which the technique of weak value amplification is implemented in order to enlarge the effect of a single photon on the quadratures of a movable mirror of an optical cavity. The photon interacts…

We propose a new learning-based approach to solve ill-posed inverse problems in imaging. We address the case where ground truth training samples are rare and the problem is severely ill-posed - both because of the underlying physics and…

Precise definitions of "weak [quantum] measurements" and "weak value" [of a quantum observable] are offered, which seem to capture the meaning of the often vague ways that these terms are used in the literature. Simple finite dimensional…

We characterize a value of an observable by a `sum rule' for generally non-commuting observables and a `product rule' when restricted to a maximal commuting subalgebra of observables together with the requirement that the value is unity for…

The exact conditions on valid pointer states for weak measurements are derived. It is demonstrated that weak measurements can be performed with any pointer state with vanishing probability current density. This condition is found both for…

We quantify the disturbance of a quantum state undergoing a sequence of observations, and particularly focus on a weak measurement followed by post-selection and compare these results to the projective counterpart. Taking into account the…

The formalism of weak measurement in quantum mechanics has revealed profound connections between measurement theory, quantum foundations, and signal processing. In this paper, we develop a pointer-free derivation of superoscillations,…

The weak value, the average result of a weak measurement, has proven useful for probing quantum and classical systems. Examples include the amplification of small signals, investigating quantum paradoxes, and elucidating fundamental quantum…

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…

The recently introduced weakly disentangled representations proposed to relax some constraints of the previous definitions of disentanglement, in exchange for more flexibility. However, at the moment, weak disentanglement can only be…

Conventional absorption spectroscopy relies on coherent laser sources, and in turn suffers from the inherent limitation of shot noise, especially in estimating weak absorption. Here we propose a measurement strategy with correlated photons…

Post-selection strategies have been proposed with the aim of amplifying weak signals, which may help to overcome detection thresholds associated with technical noise in high-precision measurements. Here we use an optical setup to…

In this letter, we consider a problem of reconstructing an unknown discrete signal taking values in a finite alphabet from incomplete linear measurements. The difficulty of this problem is that the computational complexity of the…

We show that a weak projective measurement of photon arrival time can be realized by controllable two photon interferences with photons from short-time reference pulses at a polarization beam splitter. The weak value of the projector on the…