The Bell state is a crucial resource for the realization of quantum information tasks, and when combined with orbital angular momentum (OAM), it enables a high-dimensional Hilbert space, which is essential for high-capacity quantum communication. In this study, we demonstrate the recognition of OAM Bell states using interference patterns generated by a classical light source and a single-photon source from a Sagnac interferometer-based OAM Bell state evolution device. The interference patterns exhibit a one-to-one correspondence with the input Bell states, providing conclusive evidence for the full recognition of OAM Bell states. Furthermore, we introduce machine learning to the field of Bell state recognition by proposing a neural network model capable of accurately recognizing higher order single-photon OAM Bell states, even in the undersampling case. In particular, the model’s training set includes interference patterns of OAM Bell states generated by classical light sources, yet it is able to recognize single-photon OAM Bell states with high accuracy, without relying on quantum resources during training. Our innovative application of neural networks to the recognition of single-photon OAM Bell states not only circumvents the resource consumption and experimental difficulties associated with quantum light sources but also facilitates the study of OAM-based quantum information.
Bell states are the most fundamental resource in realizing quantum information tasks and have a very unique position in quantum mechanics. Utilizing orbital angular momentum (OAM) to encode single-photon Bell states enables the realization of high-dimensional Hilbert space, which is crucial for the field of quantum information. In this paper, we design a single-photon OAM Bell-state evolution device based on the Sagnac interferometer, which can make one-to-one correspondence between the input Bell states and the output states. Moreover, we also develop a single-photon single-pixel imaging (SPI) technique, which improves spatial resolution and decreases acquisition time in the meantime, to capture interference images of output states. The results show that single-photon OAM Bell states can be fully recognized by comparing the differences of interference images. We innovatively utilize the SPI technique for single-photon OAM Bell-state recognition. This indicates that the SPI technique effectively promotes the study of quantum information based on OAM, while the quantum information based on OAM provides a clear application scenario for the SPI technique.
The generation of light containing large degrees of orbital angular momentum (OAM) has recently been demon- strated in both the classical and quantum regimes. Since there is no fundamental limit to how many quanta of OAM a single photon can carry, optical states with an arbitrarily high difference in this quantum number may, in principle, be entangled. This opens the door to investigations into high-dimensional entanglement shared between states in superpositions of nonzero OAM. Additionally, making use of non-zero OAM states can allow for a dramatic increase in the amount of information carried by a single photon, thus increasing the information capacity of a communication channel. In practice, however, it is difficult to differentiate between states with high OAM numbers with high precision. Here we investigate the ability of deep neural networks to differentiate between states that contain large values of OAM. We show that such networks may be used to differentiate be- tween nearby OAM states that contain realistic amounts of noise, with OAM values of up to 100. Additionally, we examine how the classification accuracy scales with the signal-to-noise ratio of images that are used to train the network, as well as those being tested. Finally, we demonstrate the simultaneous classification of < 100 OAM states with greater than 70 % accuracy. We intend to verify our system with experimentally-produced classi- cal OAM states, as well as investigate possibilities that would allow this technique to work in the few-photon quantum regime.
Orbital angular momentum (OAM) entanglement states have great potential in enhancing the information capacity in quantum communications. To make full use of the OAM degree of freedom, the measurement and distinction of OAM Bell states become a key step that needs to be accomplished. However, there is still no solution to achieve complete distinction of OAM Bell states at the single-photon level. Here we demonstrate the complete OAM Bell-state measurement without auxiliary photons by using linear optics. Furthermore, we propose a quantum communication network via OAM Bell-state multiplexing, perform a proof-of-principle experiment in the first- and second-order OAM subspaces for two users, and achieve average success probabilities of obtaining information of 91.6% for User-I and 89.1% for User-II. In principle, our scheme allows more users to be added by using high-order OAM Bell states. Our research extends the manipulation method for high-dimensional quantum states and paves the way for the application of OAM multiplexing in quantum communications.
Orbital angular momentum (OAM) of light has enabled quantum encoding in higher dimensional Hilbert spaces, opening up new opportunities for high capacity satellite-to-ground quantum communications. In this paper, machine learning based recognition of OAM modes for satellite-to-ground communication is proposed. Most of the machine learning models for OAM mode detection reported in literature directly take intensity and phase images of OAM modes as inputs. A novel attempt is made in the proposed work, wherein Histogram of Gradients (HOG) features are extracted from these images and fed to machine learning models. Two architectures are proposed in this paper for OAM mode detection and their performances are reported. The performances of proposed models are also compared under different atmospheric turbulence conditions, propagation distances and the results are reported. In order to evaluate the efficacy of proposed models, performance results of OAM mode detection using various other methods reported in literature are compared with the results obtained from proposed work. It is observed that the performance of proposed models are almost on par with the models reported in literature. Maximum recognition accuracy of 100% with a prediction time ranging between 83 - 157ms, was achieved using the proposed models. The proposed OAM mode detection models can be used for various other quantum communication applications too, including underwater communication.
Abstract High-dimensional (HD) entanglement of photonic orbital angular momentum (OAM) is pivotal for advancing quantum communication and information processing, but its characterization remains significant challenges due to the complexity of quantum state tomography and experimental limitations such as low photon counts caused by losses. Here, we propose a pre-trained physics-informed neural network (PTPINN) framework that enables efficient and rapid reconstruction of HD-OAM entangled states under low photon counts. Experimental results show that the fidelity of five-dimensional OAM entanglement reaches F = 0.958 ± 0.010 even with an exposure time as short as 50 ms. This highlights the capability of PTPINN to achieve high-precision quantum state reconstruction with limited photons, owing to its innovative designs, thus overcoming the reliance on high photon counts typical of traditional methods. Our method provides a practical and scalable solution for high-fidelity characterization of HD-OAM entanglement in environments with low photon numbers and high noise, paving the way for robust long-distance quantum information transmission.
Quantum memory is a key component of quantum networks. A successful development in enabling the distribution of quantum information requires the storage of single-photon light. Usually quantum information is encoded using a 2D space, spanned, for example, by the orthogonal polarization states of a photon. In this case, each photon carries a quantum bit of information. If the photon could be encoded in a high-dimensional space instead, the information carried by each photon could be increased from a bit to |
log2d| bits, where d is the dimension of the Hilbert space in which the photon is described. The channel capacity of the network and the transmission efficiency would then be greatly enlarged [1]. Moreover, storing high-dimensional states in quantum memory can reduce its sensitivity to memory coherence time [2], leading to significant improvements in storage capacity [3]. It is thus no surprise that many research groups are actively working on different physical systems for storing light encoded using a high-dimensional space. The degrees of freedom for position, linear momentum, time-bin or orbital angular momentum (OAM) of a photon can all be considered as a high-dimensional space for encoding. The photon's OAM has the most potential for encoding [4]. Electromagnetic waves have both spin and OAM. Spin angular momentum produces polarization. Photons with OAM can be regarded as helices with left and right handedness twisted to varying degrees (Fig. 1). Information is encoded using this handedness and the amount of twist. Because of the inherent infinite degrees of freedom for OAM, a photon can in principle carry an arbitrarily large amount of information, and hence the eagerness to store light encoded in OAM space. Although some work on this has been reported for different physical systems, what is lacking is a way of storing and releasing at some later time a true single photon, including its shape and structure [5–7]. Constructing this basic element of quantum memory has been a major challenge. The wavefront of an OAM light is a helical structure (left and center), with an optical vortex at its center in the intensity distribution of light (right). The vortex of light can carry non-zero OAM of any order m. OAM states of a different order are orthogonal. A group at the Key Laboratory of Quantum Information, Chinese Academy of Science, at the University of Science and Technology of China finally resolved this problem [8]. They reported on the first experimental realization of a true single-photon-carrying OAM stored via electromagnetically induced transparency (EIT) in a cold atomic ensemble (Fig. 2). With such a suitable candidate, this work indicates a means of constructing high-dimensional quantum memory. After this, similar results were reported by Laurat's group at Laboratoire Kastler Brossel, at Université Pierre et Marie Curie in France [9], where an extremely weak laser at single-photon level carrying OAM was also stored via EIT in a cold atomic ensemble. Ding et al. [8] first prepared two cold 85Rb atomic clouds in two magnetic-optical traps (MOT) using laser cooling and trapping techniques. They generated non-classical correlated photon pairs using spontaneous four-wave mixing in an atomic cloud. One photon of each pair was used as a trigger; the other mapped and stored in a second atomic cloud via EIT. Each photon to be stored carried one OAM unit. After a programed storage time, the photon was retrieved. What they achieved during storage included (1) proof that the non-classical correlation between the trigger photon and the retrieved photon is retained by demonstrating a strong violation of the Cauchy–Schwarz inequality, (2) a demonstration that the single-photon property of the signal photon is maintained by performing the Hanbury–Brown and Twiss experiment on the trigger photon, (3) proof that the spatial structure of the photon is also very well preserved by showing a high similarity between input and output, and (4) evidence, gathered by Sagnac interferometry, that the coherence of a single photon is also preserved. A heralded single photon is generated through spontaneous four-wave mixing in MOT 1 (a); this single photon carrying OAM is then stored through EIT in MOT 2 (b); (c) shows an image of the photon carrying OAM. Experimental measurements in the transverse position of the image carried by the photon before and after storage are presented in (d) and (e), respectively; (f) shows the simplified experimental setup for storage of a superposition of OAM. Interference patterns taken at different angle settings of the half-wave plate are shown in (g). The left column represents the experimental angle settings of the half-wave and the quarter-wave plates, the middle column gives the experimental results, and the right column gives results from theoretical simulations; (h) and (i) present the interference patterns of the input signal photon and the retrieved signal with plate angle, respectively. This is a significant breakthrough towards the realization of a quantum internet and, potentially, quantum computing. This work addresses the ability to generate, store, retrieve on demand an arbitrary single-photon-level photonic state encoded in OAM space. It signifies an important step in the development of practical quantum-enabled technologies, opens up the possibility for realizing high-dimensional quantum memories based on this degree of freedom of light, and will have a large impact in a broad physical community, especially in the quantum information and quantum optics communities. The Technology Review website of MIT comments on their work very positively with an article entitled ‘First Quantum Memory That Records the Shape of a Single Photon Unveiled in China’. Further, Nature Photonics selected this work as a research highlight. Clearly, memory that can preserve the spatial structure of photons will make the internet far more flexible and capable. Of course, there are still many basic problems remaining that need to be solved to build the future quantum internet, one of which is the construction of quantum memory exploiting entanglement. This derives from the fact that a quantum network needs the distribution of quantum-entangled photons over channels between different nodes [10]. A high-dimensional quantum internet needs to store OAM-entangled states and perform entanglement swapping to efficiently extend the achievable communication distances. While Ding et al. [8] reported the storage of light with OAM at the single-photon level, the photon was, however, still encoded in a 2D space. Therefore, whether it is possible to construct a high-dimensional quantum memory remains an open issue that needs to be investigated further.