Fuzzy simultaneous measurement of two polarization vector components

The advent of quantum computers threatens the security of conventional encryption schemes (e.g., those based upon the excessive amount of computational time that might be required to guess your password). Quantum encryption is intended to restore the security by basing it instead upon the impossibility of the simultaneous measurement of two noncommuting operators. I derive a measurement associated with the angular momentum lowering operator, which describes a simultaneous (yet realizable) measurement of two noncommuting spin-vector components. Correlations between two such detectors are also discussed and compared with the conventional Stern-Gerlach results.