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 operatorŝ XP +PX, i.e., a non-Gaussian measurement, is required to be fully optimal.
We find and investigate the optimal scheme of distributed quantum sensing using Gaussian states for estimation of the average of independent phase shifts. We show that the ultimate sensitivity is achievable by using an entangled symmetric Gaussian state, which can be generated using a single-mode squeezed vacuum state, a beam-splitter network, and homodyne detection on each output mode in the absence of photon loss. Interestingly, the maximal entanglement of a symmetric Gaussian state is not optimal although the presence of entanglement is advantageous as compared to the case using a product symmetric Gaussian state. It is also demonstrated that when loss occurs, homodyne detection and other types of Gaussian measurements compete for better sensitivity, depending on the amount of loss and properties of a probe state. None of them provide the ultimate sensitivity, indicating that non-Gaussian measurements are required for optimality in lossy cases. Our general results obtained through a full-analytical investigation will offer important perspectives to the future theoretical and experimental study for distributed Gaussian quantum sensing.
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 operatorxp +px, 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.
We study the sensitivity of phase estimation in a lossy Mach-Zehnder interferometer (MZI) using two general, and practical, resources generated by a laser and a nonlinear optical medium with passive optimal elements, which are readily available in the laboratory: One is a two-mode separable coherent and squeezed vacuum state at a beam splitter and the other is a two-mode squeezed vacuum state. In view of the ultimate precision given by quantum Fisher information, we show that the two-mode squeezed vacuum state can achieve a lower bound of estimation error than the coherent and squeezed vacuum state under a photon-loss channel. We further consider practical measurement schemes, homodyne detection and photon number resolving detection (PNRD), to characterize the accuracy of phase estimation in reality and find that the coherent and squeezed vacuum state largely achieves a lower bound than the two-mode squeezed vacuum in the lossy MZI while maintaining quantum enhancement over the shot-noise limit. By comparing homodyne detection and PNRD, we demonstrate that quadrature measurement with homodyne detection is more robust against photon loss than parity measurement with PNRD. We also show that double homodyne detection can provide a better tool for phase estimation than single homodyne detection against photon loss.Comment: 9+1 pages, 8 figure
Photodynamic therapy (PDT) is an effective anticancer strategy with a higher selectivity and fewer adverse effects than conventional therapies; however, shallow tissue penetration depth of light has hampered the clinical utility of PDT. Recently, reports have indicated that Cerenkov luminescence-induced PDT may overcome the tissue penetration limitation of conventional PDT. However, the effectiveness of this method is controversial because of its low luminescence intensity. Herein, we developed a radiolabeled diethylenetriaminepentaacetic acid chelated Eu3+ (Eu-DTPA)/photosensitizer (PS) loaded liposome (Eu/PS-lipo) that utilizes ionizing radiation from radioisotopes for effective in vivo imaging and radioluminescence-induced PDT. We utilized Victoria blue-BO (VBBO) as a PS and observed an efficient luminescence resonance energy transfer between Eu-DTPA and VBBO. Furthermore, 64Cu-labeled Eu lipo demonstrated a strong radioluminescence with a 2-fold higher intensity than Cerenkov luminescence from free 64Cu. In our radioluminescence liposome, radioluminescence energy transfer showed a 6-fold higher energy transfer efficiency to VBBO than Cerenkov luminescence energy transfer (CLET). 64Cu-labeled Eu/VBBO lipo (64Cu-Eu/VBBO lipo) showed a substantial tumor uptake of up to 19.3%ID/g by enhanced permeability and retention effects, as revealed by in vivo positron emission tomography. Finally, the PDT using 64Cu-Eu/VBBO lipo demonstrated significantly higher in vitro and in vivo therapeutic effects than Cerenkov luminescence-induced PDT using 64Cu-VBBO lipo. This study envisions a great opportunity for clinical PDT application by establishing the radioluminescence liposome which has high tumor targeting and efficient energy transfer capability from radioisotopes.
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