  Quantum sensing protocols typically uses a quantum sensor to sense classical
signals with the standard Ramsey inteferometry measurements. The classical
signals are often real numbers determining the sensor Hamiltonian. However, for
a senor embedded in a quantum environment, the signal to detect may be a
quantum operator on a target quantum system. There is still no systematic
method to detect such a quantum signal. Here we provide a general framework to
sense static quantum signals with a qubit sensor by the Ramsey interferometry
measurements, with the static classical signal sensing incorporated as a
special case. This framework is based on a novel approach to simultaneously
estimating the eigenvalues of the quantum signal operator with sequential
projective measurements of the sensor, which can extract useful information
about the target quantum system. The scheme can also be extended to sense ac
quantum signals with dynamical decoupling control of the sensor. As an example,
we show that a qubit sensor can simultaneously detect the individual coupling
strengths with multiple target qubits in a spin-star model.

Quantum Physics