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We examine weak measurements of arbitrary observables where the object is prepared in a mixed state and on which measurements with imperfect detectors are made. The weak value of an observable can be expressed as a conditional expectation…
Weak values and measurements have been proposed as means to achieve dramatic enhancements in metrology based on the greatly increased range of possible measurement outcomes. Unfortunately, the very large values of measurement outcomes occur…
We develop inference procedures robust to general forms of weak dependence. The procedures utilize test statistics constructed by resampling in a manner that does not depend on the unknown correlation structure of the data. We prove that…
We reveal a large spin angular splitting of light beam on reflection at the Brewster angle both theoretically and experimentally. A simple weak measurements system manifesting itself for the built-in post-selection technique is proposed to…
Quantum measurement is one of the most fascinating and discussed phenomena in quantum physics, due to the impact on the system of the measurement action and the resulting interpretation issues. Scholars proposed weak measurements to amplify…
We analytically and numerically investigate the performance of weak-value amplification (WVA) and related parameter estimation methods in the presence of temporally correlated noise. WVA is a special instance of a general measurement…
The quantum eraser variant of the double-slit experiment, and its 'delayed choice' sub-variant, are considered from the perspective of weak value and weak measurement theory (which is briefly reintroduced here). The interference fringes…
We study the weak-value amplification (WVA) in a phase measurement with an optical interferometer in which shot noise limits the sensitivity. We compute the signal and the shot noise including the full-order interaction terms of the WVA,…
We investigate a new experimental possibility of measuring the Newtonian gravitational constant $G$ by using the weak measurement. Amplification via weak measurement is one of the interesting phenomena of quantum mechanics. In this letter,…
Microvariations probe the physics and internal structure of quasars. Unpredictability and small flux variations make this phenomenon elusive and difficult to detect. Variance based probes such as the C and F tests, or a combination of both,…
An efficient Bayesian technique for estimation problems in fundamental stellar astronomy is tested on simulated data for a binary observed both astrometrically and spectroscopically. Posterior distributions are computed for the components'…
We report on the use of an interferometric weak value technique to amplify very small transverse deflections of an optical beam. By entangling the beam's transverse degrees of freedom with the which-path states of a Sagnac interferometer,…
The MICROSCOPE experiment was designed to test the weak equivalence principle in space, by comparing the low-frequency dynamics of cylindrical "free-falling" test masses controlled by electrostatic forces. We use data taken during technical…
Weak signal identification and inference are very important in the area of penalized model selection, yet they are under-developed and not well-studied. Existing inference procedures for penalized estimators are mainly focused on strong…
Recent empirical work in the field of 'weak measurements' has yielded novel ways of more directly accessing and exploring the quantum wavefunction. Measuring either position or momentum for a photon in a 'weak' manner yields a wide range of…
Progress in testing fundamental physics relies on our ability to measure exceedingly small physical quantities. Using a $^{40}$Ca$^{+}$ trapped ion system as an example we show that an exceedingly weak synthetic magnetic field (at the scale…
The weak value, introduced by Aharonov et al. to extend the conventional scope of physical observables in quantum mechanics, is an intriguing concept which sheds new light on quantum foundations and is also useful for precision measurement,…
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…
We consider the weak detection problem in a rank-one spiked Wigner data matrix where the signal-to-noise ratio is small so that reliable detection is impossible. We propose a hypothesis test on the presence of the signal by utilizing the…
A large literature has grown up around the proposed use of 'weak measurements' (i.e., unsharp measurements followed by post-selection) to allegedly provide information about hidden ontological features of quantum systems. This paper…