Weak measurement

In quantum mechanics (and computation & information), weak measurements are a type of quantum measurement that results in an observer obtaining very little information about the system on average, but also disturbs the state very little. From Busch's theorem the system is necessarily disturbed by the measurement. In the literature weak measurements are also known as unsharp, fuzzy, dull, noisy, approximate, and gentle measurements. Additionally weak measurements are often confused with the distinct but related concept of the weak value. Weak measurements were first thought about in the context of weak continuous measurements of quantum systems (i.e. quantum filtering and quantum trajectories). The physics of continuous quantum measurements is as follows. Consider using an ancilla, e.g. a field or a current, to probe a quantum system. The interaction between the system and the probe correlates the two systems. Typically the interaction only weakly correlates the system and ancilla (specifically, the interaction unitary need only to be expanded to first or second order in perturbation theory). By measuring the ancilla and then using quantum measurement theory, the state of the system conditioned on the results of the measurement can be determined. In order to obtain a strong measurement, many ancilla must be coupled and then measured. In the limit where there is a continuum of ancilla the measurement process becomes continuous in time. This process was described first by: Mensky; Belavkin; Barchielli, Lanz, Prosperi; Barchielli; Caves; Caves and Milburn. Later on Howard Carmichael and Howard M. Wiseman also made important contributions to the field. The notion of a weak measurement is often misattributed to Aharonov, Albert and Vaidman. In their article they consider an example of a weak measurement (and perhaps coin the phrase "weak measurement") and use it to motivate their definition of a weak value, which they defined there for the first time. There is no universally accepted definition of a weak measurement.