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A model is proposed for the statistical analysis of arbitrary-strength quantum measurements, based on a picture of "sampling weak values" from different configurations of the system. The model is comprised of two elements: a "local weak…
This paper aims at advancing the field of electro-sensing. It exhibits the physical mechanism underlying shape perception for weakly electric fish. These fish orient themselves at night in complete darkness by employing their active…
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…
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 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…
Weak-value amplification (WVA) has recently become an important technique for parameter estimation, owing to its ability to enhance the signal-to-noise ratio by amplifying extremely small signals with proper postselection strategies. In…
We consider the scenario where important signals are not strong enough to be separable from a large amount of noise. Such weak signals commonly exist in large-scale data analysis and play vital roles in many biomedical applications.…
In weak gravitational lensing, the image distortion caused by shear measures the projected tidal gravitational field of the deflecting mass distribution. To lowest order, the shear is proportional to the mean image ellipticity. If the image…
In this paper, the authors report a way to use concepts from statistical learning to gain an advantage in terms of error exponents while communicating over a discrete memoryless channel. The study utilizes the simulation capability of the…
Weak measurements with imaginary weak values are reexamined in light of recent experimental results. The shift of the meter, due to the imaginary part of the weak value, is derived via the probability of postselection, which allows…
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 this chapter we offer an introduction to weak values from a three-fold perspective: first, outlining the protocols that enable their experimental determination; next, deriving their correlates in the quantum formalism and, finally,…
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…
We improve the precision of the interferometric weak-value-based beam deflection measurement by introducing a power recycling mirror, creating a resonant cavity. This results in \emph{all} the light exiting to the detector with a large…
Quantum Mechanical weak values are an interference effect measured by the cross-Wigner transform W({\phi},{\psi}) of the post-and preselected states, leading to a complex quasi-distribution {\rho}_{{\phi},{\psi}}(x,p) on phase space. We…
The paper analyzes four classical signal-plus-noise models: the factor model, spiked sample covariance matrices, the sum of a Wigner matrix and a low-rank perturbation, and canonical correlation analysis with low-rank dependencies. The…
We employ the technique of weak measurement in order to enable preservation of teleportation fidelity for two-qubit noisy channels. We consider one or both qubits of a maximally entangled state to undergo amplitude damping, and show that…
The weak measurement proposed by Aharonov and his colleagues extracts information of a physical quantity of the system by the post selection as the shifts of the argument of the probe wavefunction. The shift is called the weak value and is…
We present a weak measurement protocol that permits a sensitive estimation of angular rotations based on the concept of weak-value amplification. The shift in the state of a pointer, in both angular position and the conjugate orbital…
We investigate the power of weak measurements in the framework of quantum state discrimination. First, we define and analyze the notion of weak consecutive measurements. Our main result is a convergence theorem whereby we demonstrate when…