  Quantum sensors may provide extremely high sensitivity and precision to
extract key information in a quantum or classical physical system. A
fundamental question is whether a quantum sensor is capable of uniquely
inferring unknown parameters in a system for a given structure of the quantum
sensor and admissible measurement on the sensor. In this paper, we investigate
the capability of a class of quantum sensors which consist of either a single
qubit or two qubits. A quantum sensor is coupled to a spin chain system to
extract information of unknown parameters in the system. With given
initialisation and measurement schemes, we employ the similarity transformation
approach and the Grobner basis method to prove that a single-qubit quantum
sensor cannot effectively estimate the unknown parameters in the spin chain
system while the two-qubit quantum sensor can. The work demonstrates that it is
a feasible method to enhance the capability of quantum sensors by increasing
the number of qubits in the quantum sensors for some practical applications.
