The technical merits of weak-value-amplification techniques are analyzed. We consider models of several different types of technical noise in an optical context and show that weak-value-amplification techniques (which only use a small fraction of the photons) compare favorably with standard techniques (which use all of them). Using the Fisher-information metric, we demonstrate that weak-value techniques can put all of the Fisher information about the detected parameter into a small portion of the events and show how this fact alone gives technical advantages. We go on to consider a time-correlated noise model and find that a Fisher-information analysis indicates that the standard method can have much larger information about the detected parameter than the postselected technique. However, the estimator needed to gather the information is technically difficult to implement, showing that the inefficient (but practical) signal-to-noise estimation of the parameter is usually superior. We also describe other technical advantages unique to imaginary weak-value-amplification techniques, focusing on beam-deflection measurements. In this case, we discuss combined noise types (such as detector transverse jitter, angular beam jitter before the interferometer, and turbulence) for which the interferometric weak-value technique gives higher Fisher information over conventional methods. We go on to calculate the Fisher information of the recently proposed photon-recycling scheme for beam-deflection measurements and show it further boosts the Fisher information by the inverse postselection probability relative to the standard measurement case.

In a recent Letter, Brunner and Simon proposed an interferometric scheme using imaginary weak values with a frequency-domain analysis to outperform standard interferometry in longitudinal phase shifts [Phys. Rev. Lett105, 010405 (2010)]. Here we demonstrate an interferometric scheme combined with a time-domain analysis to measure longitudinal velocities. The technique employs the near-destructive interference of non-Fourier limited pulses, one Doppler shifted due to a moving mirror in a Michelson interferometer. We achieve a velocity measurement of 400 fm/s and show our estimator to be efficient by reaching its Cramér-Rao bound.

We suggest a possible realization of a solid-state memory capacitive ͑memcapacitive͒ system. Our approach relies on the slow polarization rate of a medium between plates of a regular capacitor. To achieve this goal, we consider a multilayer structure embedded in a capacitor. The multilayer structure is formed by metallic layers separated by an insulator so that nonlinear electronic transport ͑tunneling͒ between the layers can occur. The suggested memcapacitor shows hysteretic charge-voltage and capacitance-voltage curves, and both negative and diverging capacitance within certain ranges of the field. This proposal can be easily realized experimentally and indicates the possibility of information storage in memcapacitive systems.

We experimentally investigate the relative advantages of implementing weak-value-based metrology versus standard methods. While the techniques outlined herein apply more generally, we measure small optical beam deflections both using a Sagnac interferometer with a monitored dark port (the weak-value-based technique), and by focusing the entire beam to a split detector (the standard technique). By introducing controlled external transverse detector modulations and transverse beam deflection momentum modulations, we quantify the mitigation of these sources in the weak-value-based experiment versus the standard focusing experiment. The experiments are compared using a combination of deterministic and stochastic methods. In all cases, the weak-values technique performs the same or better than the standard technique by up to two orders of magnitude in precision for our parameters. We further measure the statistical efficiency of the weak-values-based technique. By postselecting on $1\%$ of the photons, we obtain $99\%$ of the available Fisher information of the beam deflection parameter

We present a parameter estimation technique based on performing joint measurements of a weak interaction away from the weak-value-amplification approximation. Two detectors are used to collect full statistics of the correlations between two weakly entangled degrees of freedom. Without discarding of data, the protocol resembles the anomalous amplification of an imaginary-weak-value-like response. The amplification is induced in the difference signal of both detectors allowing robustness to different sources of technical noise, and offering in addition the advantages of balanced signals for precision metrology. All of the Fisher information about the parameter of interest is collected. A tunable phase controls the strength of the amplification response. We experimentally demonstrate the proposed technique by measuring polarization rotations in a linearly polarized laser pulse. We show that in the presence of technical noise the effective sensitivity and precision of a split detector is increased when compared to a conventional continuous-wave balanced detection technique.Introduction Anomalous amplification [1] has been shown to be advantageous for precision metrology. Such an amplification provides a way to increase a signal while decreasing [2] or retaining the technical-noise floor [3,4]. As a result, the sensitivity and precision of measurements limited by technical noise can be effectively improved, facilitating the saturation of the standard quantum limit. Anomalous amplification was first proposed for metrology with the introduction of the Weak Value (WV) of an observable [1,5], and parameter estimation protocols defined after it are usually known as Weak-ValueAmplification (WVA) techniques. The WV of an observable is obtained by post-selecting the state of a system after a weak interaction with a meter system. In WVA, such measurements in the system induce a discarding of data counts in the measurements of the meter. In addition to the notion that the state of the system is post-selected after the weak interaction, we consider post-selection as the process of selecting and processing desired events, which, for WVA, results in discarding data in the meter. Due to the interference of the pre-and post-selection states of the system the WV can take large complex values outside the eigenvalue spectrum of the observable, which defines the anomalous amplification in WVA. Discussion about the quantum interpretation of such a phenomenon can be found in Refs. [6][7][8][9]. Many recent applications of WVA for metrology have been done in classical optics, where the interference can be understood using standard wave mechanics [10,11].