Quantum thermometry by single qubit-probe in a thermal XY spin-chain bath

We address the estimation of temperature in a thermal XY spin-chain through quantum probe and tools of parameter estimation theory, namely the quantum Fisher information and signal to noise ratio. We focus on the situation where the probe is weakly coupled to the bath to ensure its coherent time-evolution as long as possible and, in turn, an accurate estimation of the bath temperature. Our results provide clear evidence that the estimation precision can be effectively improved by properly adjusting the probe-bath and bath-spins coupling strength. Indeed, we demonstrate that the optimum precision in the estimation of the bath temperature is achieved when the probe-bath and bath spins coupling strength are equals, leading to a long-time interaction of the probe with the bath.