The central issue in quantum parameter estimation is to find out the optimal measurement setup that leads to the ultimate lower bound of an estimation error. We address here a question of whether a Gaussian measurement scheme can achieve the ultimate bound for phase estimation in single-mode Gaussian metrology that exploits single-mode Gaussian probe states in a Gaussian environment. We identify three types of optimal Gaussian measurement setups yielding the maximal Fisher information depending on displacement, squeezing, and thermalization of the probe state. We show that the homodyne measurement attains the ultimate bound for both displaced thermal probe states and squeezed vacuum probe states, whereas for the other single-mode Gaussian probe states, the optimized Gaussian measurement cannot be the optimal setup, although they are sometimes nearly optimal. We then demonstrate that the measurement on the basis of the product quadrature operators $$\hat X\hat P + \hat P\hat X$$X ̂ P ̂ + P ̂ X ̂ , i.e., a non-Gaussian measurement, is required to be fully optimal.

We provide the quantum-mechanical description of the excitation of surface plasmon polaritons on metal surfaces by single photons. An attenuated-reflection setup is described for the quantum excitation process in which we find remarkably efficient photon-to-surface plasmon wave-packet transfer. Using a fully quantized treatment of the fields, we introduce the Hamiltonian for their interaction and study the quantum statistics during transfer with and without losses in the metal.

Photonic sensors have many applications in a range of physical settings, from measuring mechanical pressure in manufacturing to detecting protein concentration in biomedical samples. A variety of sensing approaches exist, and plasmonic systems in particular have received much attention due to their ability to confine light below the diffraction limit, greatly enhancing sensitivity. Recently, quantum techniques have been identified that can outperform classical sensing methods and achieve sensitivity below the so-called shot-noise limit. Despite this significant potential, the use of definite photon number states in lossy plasmonic systems for further improving sensing capabilities is not well studied. Here, we investigate the sensing performance of a plasmonic interferometer that simultaneously exploits the quantum nature of light and its electromagnetic field confinement. We show that, despite the presence of loss, specialised quantum resources can provide improved sensitivity and resolution beyond the shot-noise limit within a compact plasmonic device operating below the diffraction limit.

Reducing the noise below the shot-noise limit in sensing devices is one of the key promises of quantum technologies. Here, we study quantum plasmonic sensing based on an attenuated total reflection configuration with single photons as input. Our sensor is the Kretschmann configuration with a gold film, and a blood protein in an aqueous solution with different concentrations serves as an analyte. The estimation of the refractive index is performed using heralded single photons. We also determine the estimation error from a statistical analysis over a number of repetitions of identical and independent experiments. We show that the errors of our plasmonic sensor with single photons are below the shot-noise limit even in the presence of various experimental imperfections. Our results demonstrate a practical application of quantum plasmonic sensing is possible given certain improvements are made to the setup investigated, and pave the way for a future generation of quantum plasmonic applications based on similar techniques.

Quantum fidelity is a measure to quantify the closeness between two quantum states. In an operational sense, it is defined as the minimal overlap between the probability distributions of measurement outcomes and the minimum is taken over all possible positive-operator valued measures (POVMs). Quantum fidelity has been investigated in various scientific fields, but the identification of associated optimal measurements has often been overlooked despite its great importance both for fundamental interest and practical purposes. We find here the optimal POVMs for quantum fidelity between multimode Gaussian states in a closed analytical form. Our general finding is applied for selected single-mode Gaussian states of particular interest and we identify three types of optimal measurements: an excitation-number-resolving detection, a projection onto the eigenbasis of operator $\widehat{x}\widehat{p}+\widehat{p}\widehat{x}$, and a quadrature variable detection, each of which corresponds to distinct types of single-mode Gaussian states. We also show the equivalence between optimal measurements for quantum fidelity and those for quantum parameter estimation when two arbitrary states are infinitesimally close. It is applied for simplifying the derivations of quantum Fisher information and the associated optimal measurements, exemplified by displacement, phase, squeezing, and loss parameter estimation using Gaussian states.