Questions on the Structure of Perfect Matchings inspired by Quantum Physics

We state a number of related questions on the structure of perfect matchings. Those questions are inspired by and directly connected to Quantum Physics. In particular, they concern the constructability of general quantum states using modern photonic technology. For that we introduce a new concept, denoted as inherited vertex coloring. It is a vertex coloring for every perfect matching. The colors are inherited from the color of the incident edge for each perfect matching. First, we formulate the concepts and questions in pure graph-theoretical language, and finally we explain the physical context of every mathematical object that we use. Importantly, every progress towards answering these questions can directly be translated into new understanding in quantum physics.Comment: 10 pages, 4 figures, 6 questions (added suggestions from peer-review

Quantum Experiments and Graphs: Multiparty States as coherent superpositions of Perfect Matchings

We show a surprising link between experimental setups to realize high-dimensional multipartite quantum states and Graph Theory. In these setups, the paths of photons are identified such that the photon-source information is never created. We find that each of these setups corresponds to an undirected graph, and every undirected graph corresponds to an experimental setup. Every term in the emerging quantum superposition corresponds to a perfect matching in the graph. Calculating the final quantum state is in the complexity class #P-complete, thus cannot be done efficiently. To strengthen the link further, theorems from Graph Theory -- such as Hall's marriage problem -- are rephrased in the language of pair creation in quantum experiments. We show explicitly how this link allows to answer questions about quantum experiments (such as which classes of entangled states can be created) with graph theoretical methods, and potentially simulate properties of Graphs and Networks with quantum experiments (such as critical exponents and phase transitions).Comment: 6+5 pages, 4+7 figure

Quantum Experiments and Graphs III: High-Dimensional and Multi-Particle Entanglement

Quantum entanglement plays an important role in quantum information processes, such as quantum computation and quantum communication. Experiments in laboratories are unquestionably crucial to increase our understanding of quantum systems and inspire new insights into future applications. However, there are no general recipes for the creation of arbitrary quantum states with many particles entangled in high dimensions. Here, we exploit a recent connection between quantum experiments and graph theory and answer this question for a plethora of classes of entangled states. We find experimental setups for Greenberger-Horne-Zeilinger states, W states, general Dicke states, and asymmetrically high-dimensional multipartite entangled states. This result sheds light on the producibility of arbitrary quantum states using photonic technology with probabilistic pair sources and allows us to understand the underlying technological and fundamental properties of entanglement.Comment: 7 pages, 7 figures; Appendix 3 pages, 5 figure

Gouy Phase Radial Mode Sorter for Light: Concepts and Experiments

We present an in principle lossless sorter for radial modes of light, using accumulated Gouy phases. The experimental setups have been found by a computer algorithm, and can be intuitively understood in a geometric way. Together with the ability to sort angular-momentum modes, we now have access to the complete 2-dimensional transverse plane of light. The device can readily be used in multiplexing classical information. On a quantum level, it is an analog of the Stern-Gerlach experiment -- significant for the discussion of fundamental concepts in quantum physics. As such, it can be applied in high-dimensional and multi-photonic quantum experiments.Comment: main text: 7 pages, 5 figures. Supplementary Information: 5 pages, 4 figure

Phenomenology of complex structured light in turbulent air

The study of light propagation has been a cornerstone of progress in physics and technology. Recently, advances in control and shaping of light have created significant interest in the propagation of complex structures of light -- particularly under realistic terrestrial conditions. While theoretical understanding of this research question has significantly grown over the last two decades, outdoor-experiments with complex light structures are rare, and comparisons with theory have been nearly lacking. Such situations show a significant gap between theoretical models of atmospheric light behaviour and current experimental effort. Here, in an attempt to reduce this gap, we describe an interesting result of atmospheric models which are feasible for empirical observation. We analyze in detail light propagation in different spatial bases and present results of the theory that the influence of atmospheric turbulence is basis-dependent. Concretely, light propagating as eigenstate in one complete basis is stronger influenced by atmosphere than light propagating in a different, complete basis. We obtain these results by exploiting a family of the continuously adjustable, complete basis of spatial modes -- the Ince-Gauss modes. Our concrete numerical results will hopefully inspire experimental efforts and bring the theoretical and empirical study of complex light patterns in realistic scenarios closer together.Comment: 9 pages and 5 figures; supplementary: 2 pages and 6 table

Quantum Experiments and Graphs II: Quantum Interference, Computation and State Generation

We present a conceptually new approach to describe state-of-the-art photonic quantum experiments using Graph Theory. There, the quantum states are given by the coherent superpositions of perfect matchings. The crucial observation is that introducing complex weights in graphs naturally leads to quantum interference. The new viewpoint immediately leads to many interesting results, some of which we present here. Firstly, we identify a new and experimentally completely unexplored multiphoton interference phenomenon. Secondly, we find that computing the results of such experiments is #P-hard, which means it is a classically intractable problem dealing with the computation of a matrix function Permanent and its generalization Hafnian. Thirdly, we explain how a recent no-go result applies generally to linear optical quantum experiments, thus revealing important insights to quantum state generation with current photonic technology. Fourthly, we show how to describe quantum protocols such as entanglement swapping in a graphical way. The uncovered bridge between quantum experiments and Graph Theory offers a novel perspective on a widely used technology, and immediately raises many follow-up questions.Comment: 12+7 pages, 8+9 figure

Structural and biochemical insights into small RNA 3' end trimming by Arabidopsis SDN1.

A family of DEDDh 3'→5' exonucleases known as Small RNA Degrading Nucleases (SDNs) initiates the turnover of ARGONAUTE1 (AGO1)-bound microRNAs in Arabidopsis by trimming their 3' ends. Here, we report the crystal structure of Arabidopsis SDN1 (residues 2-300) in complex with a 9 nucleotide single-stranded RNA substrate, revealing that the DEDDh domain forms rigid interactions with the N-terminal domain and binds 4 nucleotides from the 3' end of the RNA via its catalytic pocket. Structural and biochemical results suggest that the SDN1 C-terminal domain adopts an RNA Recognition Motif (RRM) fold and is critical for substrate binding and enzymatic processivity of SDN1. In addition, SDN1 interacts with the AGO1 PAZ domain in an RNA-independent manner in vitro, enabling it to act on AGO1-bound microRNAs. These extensive structural and biochemical studies may shed light on a common 3' end trimming mechanism for 3'→5' exonucleases in the metabolism of small non-coding RNAs

Quantum Experiments and Hypergraphs: Multi-Photon Sources for Quantum Interference, Quantum Computation and Quantum Entanglement

We introduce the concept of hypergraphs to describe quantum optical experiments with probabilistic multi-photon sources. Every hyperedge represents a correlated photon source, and every vertex stands for an optical output path. Such general graph description provides new insights for producing complex high-dimensional multi-photon quantum entangled states, which go beyond limitations imposed by pair creation via spontaneous parametric down-conversion. Furthermore, properties of hypergraphs can be investigated experimentally. For example, the NP-Complete problem of deciding whether a hypergraph has a perfect matchin can be answered by experimentally detecting multi-photon events in quantum experiments. By introducing complex weights in hypergraphs, we show a general many-particle quantum interference and manipulating entanglement in a pictorial way. Our work paves the path for the development of multi-photon high-dimensional state generation and might inspire new applications of quantum computations using hypergraph mappings.Comment: 14pages, 11figure

SGCRNN: A ChebNet-GRU fusion model for eeg emotion recognition

The paper proposes a deep learning model based on Chebyshev Network Gated Recurrent Units, which is called Spectral Graph Convolution Recurrent Neural Network, for multichannel electroencephalogram emotion recognition. First, in this paper, an adjacency matrix capturing the local relationships among electroencephalogram channels is established based on the cosine similarity of the spatial locations of electroencephalogram electrodes. The training efficiency is improved by utilizing the computational speed of the cosine distance. This advantage enables our method to have the potential for real-time emotion recognition, allowing for fast and accurate emotion classification in real-time application scenarios. Secondly, the spatial and temporal dependence of the Spectral Graph Convolution Recurrent Neural Network for capturing electroencephalogram sequences is established based on the characteristics of the Chebyshev network and Gated Recurrent Units to extract the spatial and temporal features of electroencephalogram sequences. The proposed model was tested on the publicly accessible dataset DEAP. Its average recognition accuracy is 88%, 89.5%, and 89.7% for valence, arousal, and dominance, respectively. The experiment results demonstrated that the Spectral Graph Convolution Recurrent Neural Network method performed better than current models for electroencephalogram emotion identification. This model has broad applicability and holds potential for use in real-time emotion recognition scenarios

Distracted driving behavior recognition based on improved MobileNetV2

In recent years, research on distracted driving behavior recognition has made significant progress, with an increasing number of researchers focusing on deep-learning-based algorithms. Aiming at the problems of the existing distracted driving recognition algorithm, such as its oversized model and difficulty in adapting to low computing environments, a lightweight network MobileNetV2, is chosen as the backbone network and improved to design a distracted driving behavior detection method that is both accurate and practical. The Ghost module is employed to replace point-by-point convolution to reduce the computation, the Leaky ReLU function helps mitigate the problem of dead neurons, as it prevents gradients from becoming zero for negative inputs. Finally, the channel pruning algorithm is used to further reduce the model parameters. The experiment results on the State Farm dataset show that the model’s test accuracy can reach 94.66%, and the number of parameters is only 0.23 M. The improved model has significantly fewer parameters than the baseline model, which demonstrates the effectiveness and applicability of the method