  The major resolution-limiting factor in cryoelectron microscopy of unstained
biological specimens is radiation damage by the very electrons that are used to
probe the specimen structure. To address this problem, an electron microscopy
scheme that employs quantum entanglement to enable phase measurement precision
beyond the standard quantum limit has recently been proposed {[}Phys. Rev. A
\textbf{85}, 043810{]}. Here we identify and examine in detail measurement
errors that will arise in the scheme. An emphasis is given to considerations
concerning inelastic scattering events because in general schemes assisted with
quantum entanglement are known to be highly vulnerable to lossy processes. We
find that the amount of error due both to elastic and inelastic scattering
processes are acceptable provided that the electron beam geometry is properly
designed.
