We review recent work showing that weak values and weak measurements can be used to perform certain measurements with high accuracy and moreover can be used to directly measure the quantum wavefunction.
The ability to manipulate light has allowed scientists to verify fundamental theories of physics and to develop a new generation of technologies that use photons as a primary resource. Recent developments in quantum measurement theory have offered new alternatives to approach some of the most remarkable problems in quantum physics. Consequently, the principles of quantum mechanics have been exploited in the development of quantum technologies such as optical metrology, quantum communication, and quantum information. In recent years, weak measurements and two of its most remarkable variants: weak value amplification and direct measurement, have been developed and are considered important resources for quantum applications. In this paper, we discuss weak measurements and some significant applications of weak values. We elaborate on how distinct forms of weak values are used to observe and amplify small effects or to directly measure the quantum wave function of photons, a crucial task for schemes for quantum communication and quantum information. We also review some of the most recent methods for weak value amplification and direct measurement that our group has developed.
Weak measurements have thus far been considered instrumental in the so-called direct measurement of the quantum wave function [4J. S. Lundeen, Nature (London) 474, 188 (2011).]. Here we show that a direct measurement of the wave function can be obtained by using measurements of arbitrary strength. In particular, in the case of strong measurements, i.e., those in which the coupling between the system and the measuring apparatus is maximum, we compared the precision and the accuracy of the two methods, by showing that strong measurements outperform weak measurements in both for arbitrary quantum states in most cases. We also give the exact expression of the difference between the original and reconstructed wave function obtained by the weak measurement approach; this will allow one to define the range of applicability of such a method.