  Non-Hermitian dynamics has been widely studied to enhance the precision of
quantum sensing; and non-reciprocity can be a powerful resource for
non-Hermitian quantum sensing, as non-reciprocity allows to arbitrarily exceed
the fundamental bound on the measurement rate of any reciprocal sensors. Here
we establish fundamental limits on signal-to-noise ratio for reciprocal and
non-reciprocal non-Hermitian quantum sensing. In particular, for two-mode
linear systems with two coherent drives, an approximately attainable uniform
bound on the best possible measurement rate per photon is derived for both
reciprocal and non-reciprocal sensors. This bound is only related to the
coupling coefficients and, in principle, can be made arbitrarily large. Our
results thus demonstrate that a conventional reciprocal sensor with two drives
can simulate any non-reciprocal sensor. This work also demonstrates a clear
signature on how the excitation signals affect the signal-to-noise ratio in
non-Hermitian quantum sensing.
