 Imperfect measurements pose a challenge to BDMI and SDMI, since their rules for selecting the definite-valued properties in this case do not pick out the right properties for the apparatus (see Albert and Loewer 1990, 1991, 1993; also Ruetsche 1995). An example that clearly brings out the difficulties was formulated in the context of Stern-Gerlach experiments (Elby 1993). This argument uses the fact that the wavefunctions in the \(z\)-variable typically have infinite “tails” that introduce non-zero cross-terms; therefore, the “tail” of the wavefunction of the “down” beam may produce detection in the upper detector, and vice versa (see Dickson 1994 for a detailed discussion).