Weak value amplification: a view from quantum estimation theory that highlights what it is and what isn't

Quantum-coherence-free precision metrology by means of difference-signal amplification

The novel weak-value-amplification (WVA) scheme of precision metrology is deeply rooted in the quantum nature of destructive interference between the pre- and post-selection states. And, an alternative version, termed as joint WVA (JWVA), which employs the difference-signal from the post-selection accepted and rejected results, has been found possible to achieve even better sensitivity (two orders of magnitude higher) under some technical limitations (e.g. misalignment errors). In this work, after erasing the quantum coherence, we analyze the difference-signal amplification (DSA) technique, which serves as a classical counterpart of the JWVA, and show that similar amplification effect can be achieved. We obtain a simple expression for the amplified signal, carry out characterization of precision, and point out the optimal working regime. We also discuss how to implement the post-selection of a classical mixed state. The proposed classical DSA technique holds similar technical advantages of the JWVA and may find interesting applications in practice.

Approaching Quantum-Limited Metrology with Imperfect Detectors by Using Weak-Value Amplification

Weak-value amplification (WVA) is a metrological protocol that amplifies ultrasmall physical effects. However, the amplified outcomes necessarily occur with highly suppressed probabilities, leading to the extensive debate on whether the overall measurement precision is improved in comparison to that of conventional measurement (CM). Here, we experimentally demonstrate the unambiguous advantages of WVA that overcome practical limitations including noise and saturation of photodetection and maintain a shot-noise-scaling precision for a large range of input light intensity well beyond the dynamic range of the photodetector. The precision achieved by WVA is 6 times higher than that of CM in our setup. Our results clear the way for the widespread use of WVA in applications involving the measurement of small signals including precision metrology and commercial sensors.

Heralded Interaction Control between Quantum Systems

Quantum mechanical expectation values for subsets can differ substantially from those for the whole ensemble. This implies that the effect of interactions between two systems can be altered substantially by conditioning. Here, we experimentally demonstrate that, for two light fields ψ_{S} (signal) and ψ_{A} (ancilla) that have only weakly interacted with one another, subsequent measurements on the ancilla can produce substantial conditional amplification, attenuation, or phase shift of ψ_{S}. We observe conditional signal power changes over a large range of 30, and phase shift up to π/2, induced by measurements in ancilla bases that differ only slightly from one another. The method is generically applicable to a variety of systems, and allows one to modify or boost a given interaction by trading in success probability for interaction strength.

Anomalous vibration suppression in a weak-value-emulated heterodyne roll interferometer

We experimentally validate the vibration suppression capabilities of a weak-value-like protocol. The phase-sensitive heterodyne technique exhibits advantageous characteristics of a weak measurement including anomalous amplification in sensitivity and technical noise suppression. It does not, however, leverage the entanglement between the system and meter to amplify the signal of interest, as is typical in a weak measurement. In this formalism, we demonstrate an amplification in sensitivity to the roll angle of over 700 times. High precision roll experiments anchor numerical simulations to show that the interferometer outperforms standard interferometry by a factor of 500 in terms of peak-to-peak noise amplitude. During the measurement of a rolling stage, technical noise - primarily in the form of vibrations - is substantially attenuated. This is the first demonstration of vibration suppression capabilities that are inherent to the light from a metrology instrument instead of achieved via mechanical damping. The emulation presented in this work also identifies an avenue to achieve anomalous amplification outside of the standard weak measurement protocol.

Weak value controversy

Recent controversy regarding the meaning and usefulness of weak values is reviewed. It is argued that in spite of recent statistical arguments by Ferrie and Combes, experiments with anomalous weak values provide useful amplification techniques for precision measurements of small effects in many realistic situations. The statistical nature of weak values is questioned. Although measuring weak values requires an ensemble, it is argued that the weak value, similarly to an eigenvalue, is a property of a single pre- and post-selected quantum system.This article is part of the themed issue 'Second quantum revolution: foundational questions'.

The power of a control qubit in weak measurements

In the late 80 s, a curious effect suggested by Aharanov et al. was found to lead to an anomalous amplification based on quantum measurements of weakly coupled systems. In this paper, we investigate the quantum control of the weak value amplification of a qubit system coupled to a meter. For the qubit system, the coupling occurs via a second non-interacting qubit, initially quantum correlated with the first one. We show that for weak measurements, the control can be remotely realized via the post-selected state of the second qubit or the degree of squeezing of the meter. In our study of the quantum control of the amplification, we can easily manipulate the degree of quantum correlations between the initially correlated qubits. We find that the degree of entanglement has no effect on the quantum control of the amplification. However, we also found a clear connection between the amplification and quantum discord like measurements as well as classical correlations between the qubits. Finally, we suggest an application of the amplification control on the enhancement of the quantum measurement accuracy, e.g. measuring the relative phase of the post-selected control qubit in a more precise way, as opposed to the non-amplified case.