arXiv subjects

Yu Ning

Publications and source records attributed to Yu Ning.

8 recordsLinked to original sources

arXiv2026

On the Smallest Eigenvalues and Quantum Chromatic Numbers of Hamming Graphs and Generalizations

The smallest eigenvalues of (distance-j) Hamming graphs with distance parameter j at least half the length were completely determined by Brouwer et al. (2018). In the present work, we address the complementary regime, namely distances j strictly less than half the length, and derive asymptotic lower bounds on the smallest eigenvalue of binary Hamming graphs. For certain natural generalizations, specifically Cayley graphs defined over quaternary vector spaces, we asymptotically determine the smallest eigenvalue as well. As an application, we obtain lower bounds on the quantum chromatic number of these graphs. In particular, for the aforementioned Cayley graphs over quaternary vectors, our lower bounds for the quantum chromatic number coincide with known upper bounds.

math.CO↗

arXiv2026

A method for detecting spatio-temporal correlation anomalies of WSN nodes based on topological information enhancement and time-frequency feature extraction

Existing anomaly detection methods for Wireless Sensor Networks (WSNs) generally suffer from insufficient extraction of spatio-temporal correlation features, reliance on either timedomain or frequencydomain information alone, and high computational overhead. To address these limitations, this paper proposes a topology-enhanced spatio-temporal feature fusion anomaly detection method, TE-MSTAD. First, building upon the RWKV model with linear attention mechanisms, a Cross modal Feature Extraction (CFE) module is introduced to fully extract spatial correlation features among multiple nodes while reducing computational resource consumption. Second, a strategy is designed to construct an adjacency matrix by jointly learning spatial correlation from time-frequency domain features. Different graph neural networks are integrated to enhance spatial correlation feature extraction, thereby fully capturing spatial relationships among multiple nodes. Finally, a dualbranch network TE-MSTAD is designed for time-frequency domain feature fusion, overcoming the limitations of relying solely on the time or frequency domain to improve WSN anomaly detection performance. Testing on both public and realworld datasets demonstrates that the TE-MSTAD model achieves F1 scores of 92.52% and 93.28%, respectively, exhibiting superior detection performance and generalization capabilities compared to existing methods.

cs.NI↗

arXiv2025

Quantum Chromatic Number of Subgraphs of Orthogonality Graphs and the Distance-2 Hamming Graph

The determination of the quantum chromatic number of graphs has attracted considerable attention recently. However, there are few families of graphs whose quantum chromatic numbers are determined. A notable exception is the family of orthogonality graphs, whose quantum chromatic numbers are fully determined. In this paper, we extend these results by determining the exact quantum chromatic number of several subgraphs of the orthogonality graphs. Using the technique of combinatorial designs, we also determine the quantum chromatic number of the distance-2 Hamming graph, whose edges consist of binary vectors of Hamming distance 2, for infinitely many length.

math.CO↗

arXiv2025

On subcodes of the generalized Reed-Solomon codes

In this paper, we study a class of subcodes of codimension $1$ in the $[n,k+1]_q$ generalized Reed-Solomon (GRS) codes, whose generator matrix is derived by removing the row of degree $k-r$ from the generator matrix of the $[n,k+1]_q$ GRS codes, where $1 \le r \le k-1$. We show equivalent characterizations for this class of subcodes of the GRS codes being self-dual or near-MDS, which extends the results for $r=1$ in the literature. Along with these characterizations, families of self-dual near-MDS subcodes of the GRS codes are also proposed. Finally, for $r = 1,2$, the dual codes of the subcodes of the GRS codes are found out. In some cases, the subcodes of the GRS codes can be closed under taking dual codes. In other cases, the dual codes turn out to be the twisted GRS codes.

cs.IT↗

arXiv2025

Linear Programming Bounds on $k$-Uniform States

The existence of $k$-uniform states has been a widely studied problem due to their applications in several quantum information tasks and their close relation to combinatorial objects like Latin squares and orthogonal arrays. With the machinery of quantum enumerators and linear programming, we establish several improved non-existence results and bounds on $k$-uniform states. 1. First, for any fixed $l\geq 1$ and $q\geq 2$, we show that there exists a constant $c$ such that $(\left\lfloor{n/2}\right\rfloor-l)$-uniform states in $(\mathbb{C}^q)^{\otimes n}$ do not exist when $n\geq cq^2+o(q^2)$. The constant $c$ equals $4$ when $l=1$ and $6$ when $l=2$, which generalizes Scott's bound (2004) for $l=0$. 2. Second, when $n$ is sufficiently large, we show that there exists a constant $\theta<1/2$ for each $q \le 9$, such that $k$-uniform states in $(\mathbb{C}^q)^{\otimes n}$ exist only when $k\leq \theta n$. In particular, this provides the first bound (to the best of our knowledge) of $k$ for $4\leq q\leq 9$ and confirms a conjecture posed by Shi et al. (2023) when $q=5$ in a stronger form. 3. Finally, we improve the shadow bounds given by Shi et al. (2023) by a constant for $q = 3,4,5$ and small $n$. When $q=4$, our results can update some bounds listed in the code tables maintained by Grassl (2007--2024).

quant-ph↗

arXiv2024

Extremal Maximal Entanglement

A pure multipartite quantum state is called absolutely maximally entangled if all reductions of no more than half of the parties are maximally mixed. However, an $n$-qubit absolutely maximally entangled state only exists when $n$ equals $2$, $3$, $5$, and $6$. A natural question arises when it does not exist: which $n$-qubit pure state has the largest number of maximally mixed $\lfloor n/2 \rfloor$-party reductions? Denote this number by $Qex(n)$. It was shown that $Qex(4)=4$ in [Higuchi et al.Phys. Lett. A (2000)] and $Qex(7)=32$ in [Huber et al.Phys. Rev. Lett. (2017)]. In this paper, we give a general upper bound of $Qex(n)$ by linking the well-known Tur\'an's problem in graph theory, and provide lower bounds by constructive and probabilistic methods. In particular, we show that $Qex(8)=56$, which is the third known value for this problem.

quant-ph↗

arXiv2023

Bounds on $k$-Uniform Quantum States

Do $N$-partite $k$-uniform states always exist when $k\leq \lfloor\frac{N}{2}\rfloor-1$? In this work, we provide new upper bounds on the parameter $k$ for the existence of $k$-uniform states in $(\mathbb{C}^{d})^{\otimes N}$ when $d=3,4,5$, which extend Rains' bound in 1999 and improve Scott's bound in 2004. Since a $k$-uniform state in $(\mathbb{C}^{d})^{\otimes N}$ corresponds to a pure $((N,1,k+1))_{d}$ quantum error-correcting codes, we also give new upper bounds on the minimum distance $k+1$ of pure $((N,1,k+1))_d$ quantum error-correcting codes. Furthermore, we generalize Scott's bound to heterogeneous systems, and show some non-existence results of absolutely maximally entangled states in $\mathbb{C}^{d_1}\otimes(\mathbb{C}^{d_2})^{\otimes 2n}$.

quant-ph↗

arXiv2023

Study of neutron density fluctuation and neutron-proton correlation in Au+Au collisions using PYTHIA8/Angantyr

Utilizing the PYTHIA8 Angantyr model, which incorporates the multiple-parton interactions (MPI) based color reconnection (CR) mechanism, we study the relative neutron density fluctuation and neutron-proton correlation in Au+Au collisions at $\sqrt{s_\text{NN}}$ = 7.7, 11.5, 14.5, 19.6, 27, 39, 62.4, and 200 GeV. In this study, we have not only delved into the dependence of these two remarkable observations on rapidity, centrality, and energy, but also presented an analysis of their interplay with the MPI and CR. Our results have shown that the light nuclei yield ratio of proton, deuteron, and triton, expressed by the elegant expression $N_tN_p/N_d^2$, remains unchanged even as the rapidity coverage and collision centrality increase. Interestingly, we have also revealed that the effect of CR is entirely dependent on the presence of MPI; CR has no impact on the yield ratio if MPI is off. Our findings further demonstrate that the light nuclei yield ratio experiences a slight increase with increasing collision energy as predicted by the PYTHIA8 Angantyr model, but it cannot describe the non-monotonic trend observed by the STAR experiment. Based on the Angantyr model simulation results, it is essential not to overlook the correlation between neutron and proton fluctuations. The Angantyr model is a good baseline for studying collisions in the absence of a Quark-Gluon Plasma (QGP) system, given its lack of flow and jet quenching.

nucl-th↗