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Active optical media leading to interaction Hamiltonians of the form $ H = tilde{lambda}, (a + a^{dagger})^{zeta}$ represent a crucial resource for quantum optical technology. In this paper, we address the characterization of those nonlinear media using quantum probes, as opposed to semiclassical ones. In particular, we investigate how squeezed probes may improve individual and joint estimation of the nonlinear coupling $tilde{lambda}$ and of the nonlinearity order $zeta$. Upon using tools from quantum estimation, we show that: i) the two parameters are compatible, i.e. the may be jointly estimated without additional quantum noise; ii) the use of squeezed probes improves precision at fixed overall energy of the probe; iii) for low energy probes, squeezed vacuum represent the most convenient choice, whereas for increasing energy an optimal squeezing fraction may be determined; iv) using optimized quantum probes, the scaling of the corresponding precision with energy improves, both for individual and joint estimation of the two parameters, compared to semiclassical coherent probes. We conclude that quantum probes represent a resource to enhance precision in the characterization of nonlinear media, and foresee potential applications with current technology.
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We seek for the optimal strategy to infer the width $a$ of an infinite potential wells by performing measurements on the particle(s) contained in the well. In particular, we address quantum estimation theory as the proper framework to formulate the problem and find the optimal quantum measurement, as well as to evaluate the ultimate bounds to precision. Our results show that in a static framework the best strategy is to measure position on a delocalized particle, corresponding to a width-independent quantum signal-to-noise ratio (QSNR), which increases with delocalisation. Upon considering time-evolution inside the well, we find that QSNR increases as $t^2$. On the other hand, it decreases with $a$ and thus time-evolution is a metrological resource only when the width is not too large compared to the available time evolution. Finally, we consider entangled probes placed into the well and observe super-additivity of the QSNR: it is the sum of the single-particle QSNRs, plus a positive definite term, which depends on their preparation and may increase with the number of entangled particles. Overall, entanglement represents a resource for the precise characterization of potential wells.
We address the characterization of qubit chains and assess the performances of local measurements compared to those provided by Feynman probes, i.e. nonlocal measurements realized by coupling a single qubit regis- ter to the chain. We show that local measurements are suitable to estimate small values of the coupling and that a Bayesian strategy may be successfully exploited to achieve optimal precision. For larger values of the coupling Bayesian local strategies do not lead to a consistent estimate. In this regime, Feynman probes may be exploited to build a consistent Bayesian estimator that saturates the Cramer-Rao bound, thus providing an effective characterization of the chain. Finally, we show that ultimate bounds to precision, i.e. saturation of the quantum Cramer-Rao bound, may be achieved by a two-step scheme employing Feynman probes followed by local measurements.
Entangled measurement is a crucial tool in quantum technology. We propose a new entanglement measure of multi-mode detection, which estimates the amount of entanglement that can be created in a measurement. To illustrate the proposed measure, we perform quantum tomography of a two-mode detector that is comprised of two superconducting nanowire single photon detectors. Our method utilizes coherent states as probe states, which can be easily prepared with accuracy. Our work shows that a separable state such as a coherent state is enough to characterize a potentially entangled detector. We investigate the entangling capability of the detector in various settings. Our proposed measure verifies that the detector makes an entangled measurement under certain conditions, and reveals the nature of the entangling properties of the detector. Since the precise characterization of a detector is essential for applications in quantum information technology, the experimental reconstruction of detector properties along with the proposed measure will be key features in future quantum information processing.
Quantum probing consists of suitably exploiting a simple, small, and controllable quantum system to characterize a larger and more complex system. Here, we address the estimation of the cutoff frequency of the Ohmic spectral density of a harmonic reservoir by quantum probes. To this aim, we address the use of single-qubit and two-qubit systems and different kinds of coupling with the bath of oscillators. We assess the estimation precision by the quantum Fisher information of the sole quantum probe as well as the corresponding quantum signal-to-noise ratio. We prove that, for most of the values of the Ohmicity parameter, a simple probe such as a single qubit is already optimal for the precise estimation of the cutoff frequency. Indeed for those values, upon considering a two-qubit probe either in a Bell or in separable state, we do not find improvement to the estimation precision. However, we also showed that there exist few conditions where employing two qubits in a Bell state interacting with a common bath is more suitable for precisely estimating the cutoff frequency.
Quantum thermodynamics has emerged as a separate sub-discipline, revising the concepts and laws of thermodynamics, at the quantum scale. In particular, there has been a disruptive shift in the way thermometry, and thermometers are perceived and designed. Currently, we face two major challenges in quantum thermometry. First, all of the existing optimally precise temperature probes are local, meaning their operation is optimal only for a narrow range of temperatures. Second, aforesaid optimal local probes mandate complex energy spectrum with immense degeneracy, rendering them impractical. Here, we address these challenges by formalizing the notion of global thermometry leading to the development of optimal temperature sensors over a wide range of temperatures. We observe the emergence of different phases for such optimal probes as the temperature interval is increased. In addition, we show how the best approximation of optimal global probes can be realized in spin chains, implementable in ion traps and quantum dots.
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