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Compared with electrical neural networks, optical neural networks (ONNs) have the potentials to break the limit of the bandwidth and reduce the consumption of energy, and therefore draw much attention in recent years. By far, several types of ONNs have been implemented. However, the current ONNs cannot realize the acceleration as powerful as that indicated by the models like quantum neural networks. How to construct and realize an ONN with the quantum speedup is a huge challenge. Here, we propose theoretically and demonstrate experimentally a new type of optical convolutional neural network by introducing the optical correlation. It is called the correlated optical convolutional neural network (COCNN). We show that the COCNN can exhibit quantum speedup in the training process. The character is verified from the two aspects. One is the direct illustration of the faster convergence by comparing the loss function curves of the COCNN with that of the traditional convolutional neural network (CNN). Such a result is compatible with the training performance of the recently proposed quantum convolutional neural network (QCNN). The other is the demonstration of the COCNNs capability to perform the QCNN phase recognition circuit, validating the connection between the COCNN and the QCNN. Furthermore, we take the COCNN analog to the 3-qubit QCNN phase recognition circuit as an example and perform an experiment to show the soundness and the feasibility of it. The results perfectly match the theoretical calculations. Our proposal opens up a new avenue for realizing the ONNs with the quantum speedup, which will benefit the information processing in the era of big data.

After more than 70 years of development, holography has become an essential tool of modern optics in many applications. In fact, for various applications of different kinds of holographic techniques, stability and antijamming ability are very important. Here, optical topological structures are introduced into holographic technology, and an entirely new concept of optical topological holography is demonstrated to solve stability and antijamming problems. Based on the optical knots and links, the topological holography is not only developed in theory, but also demonstrated experimentally. In addition, a new topological holographic coding is established by regarding each knotted/linked topological structure as an information carrier. Due to the variety of knotted and linked structures and their characteristics of topological protection, such coding can have high capacity as well as robust properties. Furthermore, with writing the hologram into the liquid crystal, robust information storage of 3D topological holography is realized.

Topological photonics has been developed for more than ten years. It has been proved that the combination of topology and photons is very beneficial to the design of robust optical devices against some disturbances. However, most of the work for robust optical logic devices stays at the theoretical level. There are very few topologically-protected logic devices fabricated in experiments. Here, we report the experimental fabrication of a series of topologically-protected all-optical logic gates. Seven topologically-protected all-optical logic gates (OR, XOR, NOT, XNOR, NAND, NOR, and AND) are fabricated on silicon photonic platforms, which show strong robustness even if some disorders exist. These robust logic devices are potentially applicable in future optical signal processing and computing.

As an important imaging technique, holography has been realized with different physical dimensions of light,including polarization, wavelength, and time. Recently, quantum holography has been realized by utilizing polarization entangled state with the advantages of high robustness and enhanced spatial resolution, comparing with classical one. However, the polarization is only a two-dimensional degree of freedom, which greatly limits the capacity of quantum holography. Here, we propose a method to realize high-dimensional quantum holography by using high-dimensional orbital angular momentum (OAM) entanglement. A high capacity OAM-encoded quantum holographic system can be obtained by multiplexing a wide range of OAM-dependent holographic images. Proof-of-principle experiments with four- and six-dimensional OAM entangled states have been implemented and verify the feasibility of our idea. Our experimental results also demonstrate that the high-dimensional quantum holography shows a high robustness to classical noise. Furthermore, OAMselective holographic scheme for quantum encryption is proposed and demonstrated. Comparing with the previous schemes, the level of security of holographic imaging encryption system can be greatly improved in our high-dimensional quantum holography.

Optical knots and links have attracted great attention because of their exotic topological characteristics. Recent investigations have shown that the information encoding based on optical knots could possess robust features against external perturbations. However, as a superior coding scheme, it is also necessary to achieve a high capacity, which is hard to be fulfilled by existing knot-carriers owing to the limit number of associated topological invariants. Thus, how to realize the knot-based information coding with a high capacity is a key problem to be solved. Here, we create a type of nested vortex knot, and show that it can be used to fulfill the robust information coding with a high capacity assisted by a large number of intrinsic topological invariants. In experiments, we design and fabricate metasurface holograms to generate light fields sustaining different kinds of nested vortex links. Furthermore, we verify the feasibility of the high-capacity coding scheme based on those topological optical knots. Our work opens another way to realize the robust and high capacity optical coding, which may have useful impacts on the field of information transfer and storage., Comment: 18 pages 4 figures

Quantum computing has attracted much attention in recent decades, since it is believed to solve certain problems substantially faster than traditional computing methods. Theoretically, such an advance can be obtained by networks of the quantum operators in universal gate sets, one famous example of which is formed by CNOT gate and single qubit gates. However, realizing a device that performs practical quantum computing is tricky. This is because it requires a scalable qubit system with long coherence time and good controls, which is harsh for most current platforms. Here, we demonstrate that the information process based on a relatively stable system -- classical optical system, can be considered as an analogy of universal quantum computing. By encoding the information via the polarization state of classical beams, the optical computing elements that corresponds to the universal gate set are presented and their combination for a general information process are theoretically illustrated. Taking the analogy of two-qubit processor as an example, we experimentally verify that our proposal works well. Considering the potential of optical system for reliable and low-energy-consuming computation, our results open a new way towards advanced information processing with high quality and efficiency., Comment: 42 pages, 5 figures

The realization of all-optical integration and optical computing has always been our goal. One of the most significant challenges is to make integrated all-optical logic devices as small as possible. Here, we report the implementation of ultra-compact all-optical logic devices and integrated chips on silicon photonic platforms by topology optimization. The footprint for the fabricated all-optical logic gates with XOR and OR functions is only 1.3*1.3 {\mu}m2 (~0.84{\lambda}*0.84{\lambda}), that are the smallest all-optical dielectric logic devices ever verified in experiments in the optical communication range. The ultra-low loss of the optical signal is also demonstrated experimentally (-0.96dB). Furthermore, an integrated chip containing seven major logic gates (AND, OR, NOT, NAND, NOR, XOR, and XNOR) and a half adder is fabricated, where the associated footprint is only 1.3*4.5 {\mu}m2. Our work opens up a new path towards practical all-optical integration and optical computing., Comment: 20 pages, 5 figures, 2 table

Quantum protocols require access to large-scale entangled quantum states, due to the requirement of channel capacity. As a promising candidate, the high-dimensional orbital angular momentum (OAM) entangled states have been implemented, but only one of four OAM Bell states in each individual subspace can be distinguished. Here we demonstrate the first realization of complete OAM Bell-state measurement (OAM-BSM) in an individual subspace, by seeking the suitable unitary matrix performable using only linear optics and breaking the degeneracy of four OAM Bell states in ancillary polarization dimension. We further realize the superdense coding via our complete OAMBSM with the average success probability of ~82% and the channel capacity of ~1.1(4) bits. This work opens the window for increasing the channel capacity and extending the applications of OAM quantum states in quantum information in future., Comment: 6 pages, 4 figures

We present a quantitative method, utilising a highly sensitive quantum sensor, that extends applicability of magnetorelaxometry to biological samples at physiological temperature. The observed magnetic fields allow for non-invasive determination of physical properties of magnetic materials and their surrounding environment inside the specimen. The method is applied to American cockroaches and reveals magnetic deposits with strikingly different behaviour in alive and dead insects. We discuss consequences of this finding to cockroach magneto-reception. To our knowledge, this work represents the first characterisation of the magnetisation dynamics in live insects and helps to connect results from behavioural experiments on insects in magnetic fields with characterisation of magnetic materials in their corpses., Comment: 10 pages, 5 figures, published version

Bell-state analysis is a considerable challenge and an essential requirement for reliable implementation of quantum communication proposals. An open question is the one for the maximal fraction of successful Bell measurements. It has been pointed out that no scheme using only linear elements can implement a Bell state analyzer. Some effort has paid attention to the complete polarization-entangled Bell-state analysis using linear optics, with the aid of auxiliary means. Here we present a symmetry-broken scheme with linear optics only, without any aid of other auxiliary means, for discriminating polarization-entangled Bell states. Although our scheme is unable of realizing complete Bell-state measurement for less photon-pairs situation, it can deterministically identify four Bell states with success probabilities beyond 99.2% provided that photon-pairs are not less than 8. Our scheme as a significant breakthrough is simpler and feasible with respect to the current technology for the near-complete Bell-state analysis. Symmetry breaking is indispensable in our scheme as in other physical systems.

The Heisenberg uncertainty principle suggests that it is impossible to determine the trajectory of a quantum particle in the same way as a classical particle. However, we may still yield insight into novel behavior of photons based on the average photon trajectories (APTs). Here we explore the APTs of photons carrying spin angular momentum (SAM) and/or orbital angular momentum (OAM) under the paraxial condition. We define the helicity and differential helicity for unveiling the three-dimensional spiral structures of the APTs of photons. We clarify the novel behaviors of the APTs caused by the SAM and OAM as well as the SAM-OAM coupling. The APT concept is very helpful for profoundly understanding the motion of trapped particles and for elucidating other physical systems. Due to the presence of the helical path caused by the SAM and/or the OAM, the actual traveling distance of the photons might be much longer than the geometric distance.

Photons may have homogeneous polarization and may carry quantized orbital angular momentum (OAM). Photon entanglement has been realized in various degrees of freedom such as polarization and OAM. Using a pair of orthogonally polarized states carrying opposite-handedness quantized OAMs could create "quantized" vector polarization states with space-variant polarization structures. It is thus possible to extend the polarization degree of freedom from two dimensional space to indefinite dimensional discrete Hilbert space. We present a class of vector-polarization entangled Bell states, which use the spatial modes of the vector fields with space-variant polarization structure. We propose a scheme of creating the vector-polarization entangled Bell states using a Sagnac interferometer. We also design an analyzer for identifying the vector-polarization entangled Bell states. Such a class of entanglement is important for quantum information science and technology, and fundamental issues of quantum theory, due to its advantage of the increase in information capacity.