On the validity of weak measurement applied for precision measurement

Abstract

We present a general framework of examining the validity of weak measurement—the standard procedure to acquire Aharonov’s weak value—which has been used intensively in recent years for precision measurement, exploiting the amplification mechanism available for the weak value. Our framework allows one to deal systematically with various causes of uncertainties intrinsic to the actual measurement process as well as those found in the theoretical analysis employed to describe the system. Using our framework, we examine in detail the two seminal experiments, Hosten’s detection measurement of the spin Hall effect of light [Hosten and Kwiat 2008 Science 319 787] and Dixon’s ultra sensitive beam deflection measurement [Dixon et al 2009 Phys. Rev. Lett. 102 173601]. Our analysis shows that their results are well within the range of amplification (actually in the vicinity of the optimal point) where the weak measurements are valid. This suggests that our framework is both practical and sound, and may be useful to determine beforehand the possible extent of amplification in the future weak measurement experiments.