ObjectiveAs the primary tool for high-precision phase measurement, optical phase sensing has an important application in fields such as target tracking and phased-array radar. Currently, phase sensing primarily relies on distributed quantum sensing protocols to achieve high-precision phase measurement across multiple sensing nodes. Research indicates that utilizing entangled state networks can further improve phase estimation accuracy, reaching measurement sensitivities beyond the shotnoise limit. However, as the number of sensing nodes increases, system losses also increase, leading to a decrease in the precision of optical phase sensing. This becomes a major factor constraining the practical application of quantum sensing. To investigate the potential application of optical phase sensing with fewer nodes, exploration of the angle of arrival (AoA) in dual-node optical sensing is conducted.MethodThis paper presents an AoA estimation protocol based on phase squeezed states. AoA estimation is transformed into a phase difference estimation problem between two sensing nodes. By deriving the phase difference between two sensing nodes under the beam splitter model, it is found that the measurement accuracy of phase difference is not only limited by the squeezing degree of the phase squeezed state, but also related to the vacuum fluctuations introduced by the beam splitter network. To explore the application of AoA in dual-node optical sensing, an experimental setup for AoA estimation based on phase squeezed states is constructed. The preparation of phase squeezed state is carried out using an optical parametric oscillator (OPO). The OPO adopts a single-resonator structure, allowing the 532 nm pump light to pass through the cavity twice and the 1 064 nm fundamental light to resonate inside the cavity. To achieve stable output of phase squeezed state, the OPO should operate in an amplification state. Therefore, the Pound-Drever-Hall (PDH) locking technique is employed to lock the relative phase between the seed light and the pump light. In order to realize dual-node optical phase sensing, a variable beam splitter is used to split the squeezed state light into two sensing nodes, resulting in entanglement between the two sensing nodes. By controlling the splitting ratio between the two sensing nodes, the response characteristics of the entanglement degree of the dual sensing nodes with respect to the reflectance R of the variable beam splitter are investigated.Results and DiscussionsTo maximize the quantum enhancement advantage of phase squeezed states in AoA estimation, the entanglement degree of the dual sensing nodes is measured with the reflectance R varied. The results indicate that when R is 0.5, the quantum entanglement properties between the two sensing nodes are maximized. As R deviates from 0.5, the entanglement decreases due to the vacuum fluctuations introduced by the beam splitter. To validate the feasibility of phase estimation based on phase squeezed states, the optical phase shift is measured for different modulation phases. The results demonstrate a sinusoidal trend in the phase shift as the modulation phase varies from 0 to 2π, consistent with theoretical predictions. Furthermore, compared to classical protocols, the noise fluctuations in phase difference estimation based on phase squeezed states exhibit a significant reduction, highlighting the quantum enhancement advantage of arrival angle estimation protocols based on non-classical states.ConclusionThis paper proposes an AoA estimation protocol based on entangled state optical fields. A continuous solid-state laser source with a central wavelength of 1 064 nm, an optical parametric oscillator, and a variable beam splitter are used to prepare entangled state optical fields with a maximum entanglement of (6.1±0.2) dB. By controlling the optical phase of the sensing nodes, precise scanning of the 0～2π phase for two sensing nodes is achieved, enabling AoA estimation beyond the shot noise limit. Compared to classical protocols, this protocol can suppress the fluctuations of noise in AoA estimation to at least 5.9 dB below the shot noise baseline, increasing the accuracy of AoA estimation by over 74.1%. This protocol is expected to improve the precision of phase estimation beyond the shot noise limit, providing a theoretical and experimental basis for higher-precision spatial positioning and quantum ranging technologies.