  Quantum sensors offer the capability to reach unprecedented precision by
operating at the standard quantum limit (SQL) or beyond by using quantum
entanglement. But an emerging class of quantum sensors that use Rydberg
electromagnetically-induced transparency (EIT) to detect rf electric fields
have yet to reach the SQL. In this work we prove that this discrepancy is due
to fundamental limitations in the EIT probing mechanism. We derive the optimum
sensitivity of a three-level quantum sensor based on EIT, or more generally
coherent spectroscopy, and compare this to the SQL. We apply a minimal set of
assumptions, while allowing strong probing fields, thermal broadening, and
large optical depth. We derive the optimal laser intensities and optical depth,
providing specific guidelines for sensitive operation under common experimental
conditions. Clear boundaries of performance are established, revealing that
ladder-EIT can not achieve the SQL due to unavoidable absorption loss. The
results may be applied to any EIT-based quantum sensor, but we particularly
emphasize our results' importance to the growing field of Rydberg quantum
sensing.
