Disturbance in weak measurements and the difference between quantum and classical weak values

Abstract

The role of measurement induced disturbance in weak measurements is of central importance for the interpretation of the weak value. Uncontrolled disturbance can interfere with the postselection process and make the weak value dependent on the details of the measurement process. Here we develop the concept of a generalized weak measurement for classical and quantum mechanics. The two cases appear remarkably similar, but we point out some important differences. A priori it is not clear what the correct notion of disturbance should be in the context of weak measurements.We consider three different notions and get three different results: (1) For a 'strong' definition of disturbance, we find that weak measurements are disturbing. (2) For a weaker definition we find that a general class of weak measurements are non-disturbing, but that one gets weak values which depend on the measurement process. (3) Finally, with respect to an operational definition of the 'degree of disturbance', we find that the AAV weak measurements are the least disturbing, but that the disturbance is always non-zero.

Weak values as interference phenomena

“…(1) as an estimate is that it may exceed the eigenvalue range ofÂ; such strange behavior is illustrated as the shaded areas in Figure 1. As discussed in the introduction, a classical conditioned estimate may show such anomalous behavior only if the estimation procedure is noisy and if what is being estimated is disturbed in the interval [0, T ] [14,15,17,23,24]. The question raised in Ref.…”

“…In fact, every element of this simple example of how intermediate disturbance can cause strange postselected averages of noisy signals has been previously demonstrated, and corroborates our published work: Not only did we emphasize a similar disturbance example using a colored marble in our systematic investigation of generalized observable measurements [13,14], but we also carefully highlighted the potential role of invasive measurements in studies linking strange conditioned averages (including weak values) to violations of generalized Leggett-Garg inequalities [15][16][17][18][19] (which were designed to test for "quantum" behavior in macroscropic systems [20][21][22]). It is now well-established that any hidden-variable model that can produce strange conditioned averages like the weak value must include some form of intermediate disturbance (see also [23,24]). The more interesting question to raise is not whether a particular strange conditioned average may be explained as classical disturbance, but rather whether such models of disturbance can also reproduce the complete behavior of the weak value as its physical parameters are varied.…”

Weak value beyond conditional expectation value of the pointer readings

“…Still, a controversy regarding the usefulness of anomalous weak values for parameter estimation and metrology compared to conventional methods based on strong measurements arose [15][16][17][18][19][20][21][22][23][24][25][26]. Moreover, even the quantum nature of weak values was questioned [27][28][29][30][31][32][33][34].…”

Weak values are quantum: you can bet on it

“…An important observation is that one obtains the Aharonov-Albert-Vaidman weak value as the weak measurement limit of a conditioned average in a wide class of models, where the detector minimally disturbs the system. 4,11 How to define weak values as minimal backaction limit over a wide family of quantum measurement protocols is the subject of current research.…”