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 us
ing 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.
We address the use of neural networks (NNs) in classifying the environmental parameters of single-qubit dephasing channels. In particular, we investigate the performance of linear perceptrons and of two non-linear NN architectures. At variance with t
ime-series-based approaches, our goal is to learn a discretized probability distribution over the parameters using tomographic data at just two random instants of time. We consider dephasing channels originating either from classical 1/f{alpha} noise or from the interaction with a bath of quantum oscillators. The parameters to be classified are the color {alpha} of the classical noise or the Ohmicity parameter s of the quantum environment. In both cases, we found that NNs are able to exactly classify parameters into 16 classes using noiseless data (a linear NN is enough for the color, whereas a single-layer NN is needed for the Ohmicity). In the presence of noisy data (e.g. coming from noisy tomographic measurements), the network is able to classify the color of the 1/f{alpha} noise into 16 classes with about 70% accuracy, whereas classification of Ohmicity turns out to be challenging. We also consider a more coarse-grained task, and train the network to discriminate between two macro-classes corresponding to {alpha} lessgtr 1 and s lessgtr 1, obtaining up to 96% and 79% accuracy using single-layer NNs.
We put forward a measure based on Gaussian steering to quantify the non-Markovianity of continuous-variable (CV) Gaussian quantum channels. We employ the proposed measure to assess and compare the non-Markovianity of a quantum Brownian motion (QBM) c
hannel, originating from the interaction with Ohmic and sub-Ohmic environments with spectral densities described by a Lorentz-Drude cutoff, both at high and low temperatures, showing that sub-Ohmic, high temperature environments lead to highly non-Markovian evolution, with cyclic backflows of Gaussian steerability from the environment to the system. Our results add to the understanding of the interplay between quantum correlations and non-Markovianity for CV systems, and could be implemented at the experimental level to quantify non-Markovianity in some physical scenarios.
We address the discrimination of structured baths at different temperatures by dephasing quantum probes. We derive the exact reduced dynamics and evaluate the minimum error probability achievable by three different kinds of quantum probes, namely a q
ubit, a qutrit and a quantum register made of two qubits. Our results indicate that dephasing quantum probes are useful in discriminating low values of temperature, and that lower probabilities of error are achieved for intermediate values of the interaction time. A qutrit probe outperforms a qubit one in the discrimination task, whereas a register made of two qubits does not offer any advantage compared to two single qubits used sequentially.
Nonclassicality according to the singularity or negativity of the Glauber P-function is a powerful resource in quantum information, with relevant implications in quantum optics. In a Gaussian setting, and for a system of two modes, we explore how P-n
onclassicality may be conditionally generated or influenced on one mode by Gaussian measurements on the other mode. Starting from the class of two-mode squeezed thermal states (TMST), we introduce the notion of nonclassical steering (NS) and the graphical tool of Gaussian triangoloids. In particular, we derive a necessary and sufficient condition for a TMST to be nonclassically steerable, and show that entanglement is only necessary. We also apply our criterion to noisy propagation of a twin-beam state, and evaluate the time after which NS is no longer achievable. We then generalize the notion of NS to the full set of Gaussian states of two modes, and recognize that it may occur in a weak form, which does not imply entanglement, and in a strong form that implies EPR-steerability and, a fortiori, also entanglement. These two types of NS coincide exactly for TMSTs, and they merge with the previously known notion of EPR steering. By the same token, we recognize a new operational interpretation of P-nonclassicality: it is the distinctive property that allows one-party entanglement verification on TMSTs.
This is a tutorial aimed at illustrating some recent developments in quantum parameter estimation beyond the Cram`er-Rao bound, as well as their applications in quantum metrology. Our starting point is the observation that there are situations in cla
ssical and quantum metrology where the unknown parameter of interest, besides determining the state of the probe, is also influencing the operation of the measuring devices, e.g. the range of possible outcomes. In those cases, non-regular statistical models may appear, for which the Cram`er-Rao theorem does not hold. In turn, the achievable precision may exceed the Cram`er-Rao bound, opening new avenues for enhanced metrology. We focus on quantum estimation of Hamiltonian parameters and show that an achievable bound to precision (beyond the Cram`er-Rao) may be obtained in a closed form for the class of so-called controlled energy measurements. Examples of applications of the new bound to various estimation problems in quantum metrology are worked out in some details.
We introduce a fidelity-based measure $text{D}_{text{CQ}}(t)$ to quantify the differences between the dynamics of classical (CW) and quantum (QW) walks over a graph. We provide universal, graph-independent, analytic expressions of this quantum-classi
cal dynamical distance, showing that at short times $text{D}_{text{CQ}}(t)$ is proportional to the coherence of the walker, i.e. a genuine quantum feature, whereas for long times it depends only on the size of the graph. At intermediate times, $text{D}_{text{CQ}}(t)$ does depend on the graph topology through its algebraic connectivity. Our results show that the difference in the dynamical behaviour of classical and quantum walks is entirely due to the emergence of quantum features at short times. In the long time limit, quantumness and the different nature of the generators of the dynamics, e.g. the open system nature of CW and the unitary nature of QW, are instead contributing equally.
We address the use of optical parametric oscillator (OPO) to counteract phase-noise in quantum optical communication channels, and demonstrate reduction of phase diffusion for coherent signals travelling through a suitably tuned OPO. In particular, w
e theoretically and experimentally show that there is a threshold value on the phase-noise, above which OPO can be exploited to squeeze phase noise. The threshold depends on the energy of the input coherent state, and on the relevant parameters of the OPO, i.e. gain and input/output and crystal loss rates.
It is often the case that the environment of a quantum system may be described as a bath of oscillators with Ohmic density of states. In turn, the precise characterization of these classes of environments is a crucial tool to engineer decoherence or
to tailor quantum information protocols. Recently, the use of quantum probes in characterizing Ohmic environments at zero-temperature has been discussed, showing that a single qubit provides precise estimation of the cutoff frequency. On the other hand, thermal noise often spoil quantum probing schemes, and for this reason we here extend the analysis to complex system at thermal equilibrium. In particular, we discuss the interplay between thermal fluctuations and time evolution in determining the precision {attainable by} quantum probes. Our results show that the presence of thermal fluctuations degrades the precision for low values of the cutoff frequency, i.e. values of the order $omega_c lesssim T$ (in natural units). For larger values of $omega_c$ decoherence is mostly due to the structure of environment, rather than thermal fluctuations, such that quantum probing by a single qubit is still an effective estimation procedure.
We address the problem of sensing the curvature of a manifold by performing measurements on a particle constrained to the manifold itself. In particular, we consider situations where the dynamics of the particle is quantum mechanical and the manifold
is a surface embedded in the three-dimensional Euclidean space. We exploit ideas and tools from quantum estimation theory to quantify the amount of information encoded into a state of the particle, and to seek for optimal probing schemes, able to actually extract this information. Explicit results are found for a free probing particle and in the presence of a magnetic field. We also address precision achievable by position measurement, and show that it provides a nearly optimal detection scheme, at least to estimate the radius of a sphere or a cylinder.
