No abstract

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 equilibrium condition. Here, we discuss a way to generalize this relation in a non-equilibrium regime, taking into account purely quantum effects such as coherence. We support our findings with an experimental photonic simulation.Introduction:-Identifying strategies for improving the measurement precision by means of quantum resources is the purpose of Quantum Metrology [1][2][3]. In particular, through the Quantum Cramér-Rao Bound (QCRB), it sets ultimate limits on the best accuracy attainable in the estimation of unknown parameters even when the latter are not associated with observable quantities. These considerations have attracted an increasing attention in the field of quantum thermodynamics, where an accurate control of the temperature is highly demanding [4][5][6][7][8]. Besides the emergence of primary and secondary thermometers based on precisely machined microwave resonators [9,10], recent efforts have been made aiming at measuring temperature at even smaller scales, where nanosize thermal baths are higly sensitives to disturbances induced by the probe [11][12][13][14][15][16][17]. Some paradigmatic examples of nanoscale thermometry involve nanomechanical resonators [19], quantum harmonic oscillators [20] or atomic condensates [21][22][23] (also in conjunction with estimation of chemical potential [24]). In this context the analysis of quantum properties needs to be taken into account in order to establish, and eventually enhance, metrological precision [18,[25][26][27][28][29].In a conventional approach to thermometry, an external bath B at thermal equilibrium is typically indirectly probed via an ancillary system, the thermometer S, that is placed into weak-interaction with the former. Assuming hence that the thermometer reaches the thermal equilibrium configuration without perturbing B too much, the Einstein Theory of Fluctuations (ETF) can be used to characterize the sensitivity of the procedure in terms of the heat capacity of S which represents its thermal susceptibility to the perturbation imposed by the bath [30][31][32]. Since this last is an equilibrium property, one should not expect it to hold in non-equilibrium regimes. However thermometry schemes that do not need a full thermalization of the probe have been recognized to offer higher sensitivities in temperature estimation [33].Thus, if on the one hand the QCRB can still be used as the proper tool to gauge the measurement uncertainty on the bath temperature, on the other hand establishing a direct link between this approach and the thermodynamic properties of the probe is still an open question. Furthermore, the advantages pointed out in [33] are conditional on precisely addressing the probe during its evolution, a task which might be demanding in real experiments [28]. Here S i...

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 probesqubits -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.

Clausius inequality has deep implications for reversibility and the arrow of time. Quantum theory is able to extend this result for closed systems by inspecting the trajectory of the density matrix on its manifold. Here we show that this approach can provide an upper and lower bound to the irreversible entropy production for open quantum systems as well. These provide insights on the thermodynamics of the information erasure. Limits of the applicability of our bounds are discussed, and demonstrated in a quantum photonic simulator.

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)PLRAAN1050-294710.1103/PhysRevA.91.012331] 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.