Single-qubit thermometry presents the simplest tool to measure the temperature of thermal baths with reduced invasivity. At thermal equilibrium, the temperature uncertainty is linked to the heat capacity of the qubit, however, the best precision is achieved outside the equilibrium condition. Here, we discuss a way to generalize this relation in a nonequilibrium regime, taking into account purely quantum effects such as coherence. We support our findings with an experimental photonic simulation.

Standard thermometry employs the thermalization of a probe with the system of interest. This approach can be extended by incorporating the possibility of using the nonequilibrium states of the probe and the presence of coherence. Here, we illustrate how these concepts apply to the single-qubit thermometer introduced by Jevtic et al. [ Phys. Rev. A 91, 012331 (2015)] by performing a simulation of the qubit-environment interaction in a linear-optical device. We discuss the role of the coherence and how this affects the usefulness of nonequilibrium conditions. The origin of the observed behavior is traced back to how the coherence affects the propensity to thermalization. We discuss this aspect by considering the availability function.

Optical sensors based on quantum light need to work even in the presence of imperfections. Here we discuss how to address the presence of noise by measuring multiple parameters at once: those we seek to monitor and those linked to the imperfections. Our method is applied to the investigation of the optical activity of sugary solutions limited by reduced visibility. These studies introduce multiparameter estimation as a viable approach to allow for robust operation of quantum sensors as they are developed from fundamental research to technology.

Careful tailoring the quantum state of probes offers the capability of investigating matter at unprecedented precisions. Rarely, however, the interaction with the sample is fully encompassed by a single parameter, and the information contained in the probe needs to be partitioned on multiple parameters. There exist, then, practical bounds on the ultimate joint-estimation precision set by the unavailability of a single optimal measurement for all parameters. Here, we discuss how these considerations are modified for two-level quantum probes — qubits — by the use of two copies and entangling measurements. We find that the joint estimation of phase and phase diffusion benefits from such collective measurement, while for multiple phases no enhancement can be observed. We demonstrate this in a proof-of-principle photonics setup.

Introducing quantum sensors as a solution to real world problems demands reliability and controllability outside of laboratory conditions. Producers and operators ought to be assumed to have limited resources readily available for calibration, and yet, they should be able to trust the devices. Neural networks are almost ubiquitous for similar tasks for classical sensors: here we show the applications of this technique to calibrating a quantum photonic sensor. This is based on a set of training data, collected only relying on the available probe states, hence reducing overhead. We found that covering finely the parameter space is key to achieving uncertainties close to their ultimate level. This technique has the potential to become the standard approach to calibrate quantum sensors.