  We investigate in the framework of quantum noise theory how the striking
boundary-sensitivity recently discovered in the context of non-Hermitian (NH)
topological phases may be harnessed to devise novel quantum sensors.
Specifically, we study a quantum-optical setting of coupled modes arranged in
an array with broken ring geometry that would realize a NH topological phase in
the classical limit. Using methods from quantum-information theory of Gaussian
states, we show that a small coupling induced between the ends of the broken
ring may be detected with a precision that increases exponentially in the
number of coupled modes, e.g. by heterodyne detection of two output modes.
While this robust effect only relies on reaching a NH topological regime, we
identify a resonance phenomenon without direct classical counterpart that
provides an experimental knob for drastically enhancing the aforementioned
exponential growth. Our findings pave the way towards designing quantum NH
topological sensors (QUANTOS) that may observe with high precision any physical
observable that couples to the boundary conditions of the device.
