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In the realm of large-scale point cloud registration, designing a compact symbolic representation is crucial for efficiently processing vast amounts of data, ensuring registration robustness against significant viewpoint variations and occlusions. This paper introduces a novel point cloud registration method, i.e., QuadricsReg, which leverages concise quadrics primitives to represent scenes and utilizes their geometric characteristics to establish correspondences for 6-DoF transformation estimation. As a symbolic feature, the quadric representation fully captures the primary geometric characteristics of scenes, which can efficiently handle the complexity of large-scale point clouds. The intrinsic characteristics of quadrics, such as types and scales, are employed to initialize correspondences. Then we build a multi-level compatibility graph set to find the correspondences using the maximum clique on the geometric consistency between quadrics. Finally, we estimate the 6-DoF transformation using the quadric correspondences, which is further optimized based on the quadric degeneracy-aware distance in a factor graph, ensuring high registration accuracy and robustness against degenerate structures. We test on 5 public datasets and the self-collected heterogeneous dataset across different LiDAR sensors and robot platforms. The exceptional registration success rates and minimal registration errors demonstrate the effectiveness of QuadricsReg in large-scale point cloud registration scenarios. Furthermore, the real-world registration testing on our self-collected heterogeneous dataset shows the robustness and generalization ability of QuadricsReg on different LiDAR sensors and robot platforms. The codes and demos will be released at \url{https://levenberg.github.io/QuadricsReg}., Comment: 25 pages, 17 figures

Squeezed spin states have important applications in quantum metrology and sensing. It has been shown by S{\o}rensen and M{\o}lmer [Phys. Rev. A 66, 022314(2002)] that an effective one-axis-twisting interaction can be realized in a cavity setup via a double off-resonance stimulated Raman scattering, resulting in a noise reduction scaling $\propto 1/N^{2/3}$ with $N$ being the atom number. Here, we show that, by making an appropriate change of the initial input spin state, it is possible to produce a one-axis-twisting spin squeezing via a \emph{single} off-resonance stimulated Raman scattering, which thus can greatly simplify the realistic implementation. We also show that the one-axis-twisting interaction can be transformed into a more efficient two-axis-twisting interaction by rotating the collective spin while coupling to the cavity, yielding a Heisenberg limited noise reduction $\propto1/N$. Considering the noise effects due to atomic decoherence and cavity decay, we find that substantial squeezing is still attainable with current laboratory techniques., Comment: 8 pages, 2 figures

The ability to efficiently realize storage and readout of optical squeezed states plays a key roll in continuous-variables quantum information processing. Here we study the quantum memory (QM) for squeezed state of propagating light in atoms based on the hybrid photon echo re-phasing (HYPER). The optical quantum state is recorded in two sublevels of the ground state of an atomic ensemble to realize long-lived QM. Taking into account the noise effect due to atomic decay, our estimation indicates that, with currently available technique, high fidelities larger than the classical fidelity threshold 81.5 % are obtainable. Our work provides some practical guidance for realization of efficient and faithful photon-echo-based memory for squeezed light.

The continuous-variable controlled-Z gate is a canonical two-mode gate for universal continuous-variable quantum computation. It is considered as one of the most fundamental continuous-variable quantum gates. Here we present a scheme for realizing continuous-variable controlled-Z gate between two optical beams using an atomic ensemble. The gate is performed by simply sending the two beams propagating in two orthogonal directions twice through a spin-squeezed atomic medium. Its fidelity can run up to one if the input atomic state is infinitely squeezed. Considering the noise effects due to atomic decoherence and light losses, we show that the observed fidelities of the scheme are still quite high within presently available techniques., Comment: 7 pages, 3 figures, to appear in Physical Review A