  Unconventional properties of non-Hermitian systems, such as the existence of
exceptional points, have recently been suggested as a resource for sensing. The
impact of noise and utility in quantum regimes however remains unclear. In this
work, we analyze the parametric-sensing properties of linear coupled-mode
systems that are described by effective non-Hermitian Hamiltonians. Our
analysis fully accounts for noise effects in both classical and quantum
regimes, and also fully treats a realistic and optimal measurement protocol
based on coherent driving and homodyne detection. Focusing on two-mode devices,
we derive fundamental bounds on the signal power and signal-to-noise ratio for
any such sensor. We use these to demonstrate that enhanced signal power
requires gain, but not necessarily any proximity to an exceptional point.
Further, when noise is included, we show that non-reciprocity is a powerful
resource for sensing: it allows one to exceed the fundamental bounds
constraining any conventional, reciprocal sensor. We analyze simple two-mode
non-reciprocal sensors that allow this parametrically-enhanced sensing, but
which do not involve exceptional point physics.
