Let's say I start out with a (spin) neutral electron beam. Now, I can place an up/down Stein-Gerlach spin filter/detector in the beam so that I have a running tally of the "up" electrons, and a spin-down exit beam. Since the measuring device is accumulating spin-up electrons, it should also be accumulating net spin-up. Now, let's say I have a terminal for the beam, which splits the beam into left and right spin electrons using a Stein-Gerlach device, and takes counts of both. Now, the terminal is interacting with (what I expect to be) a roughly equal number of spin-up and spin-down electrons, so there should be no net accumulation of spin in the terminal. This seems problematic because the filter is accumulating net spin without conservation of spin. What am I missing?