arXiv subjects

Wenjie Zhong

Publications and source records attributed to Wenjie Zhong.

13 recordsLinked to original sources

arXiv2026

There Are No Nontrivial Perfect Codes in the Johnson Scheme

In his pioneering work from 1973, Delsarte conjectured that the Johnson scheme J$(n,w)$ admits no nontrivial perfect codes. Although related existence problems have been resolved in several other association schemes, the problem in the Johnson scheme remained open. We prove Delsarte's conjecture: no nontrivial e-perfect code exists in any Johnson scheme. The proof combines divisibility properties of balls in the scheme, bounds on the strength of designs associated with perfect codes, the roots of Lloyd polynomials, and explicit results on primes and linear forms in logarithms.

math.CO↗

arXiv2026

The Last Seven Open Radii for Perfect Codes in the Johnson Scheme

Delsarte (1973) conjectured that there are no nontrivial perfect codes in the Johnson scheme. In this paper, we prove that there are no nontrivial $e$-perfect codes in the Johnson scheme for $e\in\{1,2,4,9,10,12,16\}$. This paper complements "Perfect Codes in the Johnson Scheme Hardly Exist", thus proving Delsarte's conjecture completely.

math.CO↗

arXiv2026

Tomography of a Macroscopic Quantum State influenced by Classical Self-Gravity

Macroscopic optomechanical systems offer a promising testbed for distinguishing whether gravity acts as a quantum interaction or as a classical field. Schrodinger-Newton (SN) theory is the nonrelativistic limit of semi-classical gravity where quantum matter couples to classical gravity. Based on SN theory, this work investigates how classical self-gravity affects continuous quantum state tomography of a macroscopic mechanical oscillator monitored by variable-angle homodyne detection. In the Schrodinger-Newton (SN) theory, the measurement record arises from a different conditional test mass dynamics from that in quantum-gravity (QG)/standard quantum mechanics, consequently, applying the QG-optimised reconstruction map introduces an additional state-dependent contribution. We show that this contribution makes the reconstructed covariance depend on the chosen set of tomography angles and can drive the SN covariance--after QG filtering--outside the standard Gaussian-covariance domain set by the Heisenberg uncertainty principle. We quantify the resulting QG-SN distinguishability via the Hellinger distance and analyse its dependence on measurement strength and temperature. We then formulate the same issue in the broader setting of nonlinear quantum mechanics: when the system's conditional dynamics during the readout process depends on the state being inferred, the tomographic map acquires nonlinear, model-dependent corrections to the usual Radon or Gaussian reconstruction map.

quant-ph↗

arXiv2025

Quantitative Frameproof Codes and Hypergraphs

Frameproof codes are a class of secure codes introduced by Boneh and Shaw in the context of digital fingerprinting, and have been widely studied from a combinatorial point of view. In this paper, we study a quantitative extension of frameproof codes and hypergraphs, referred to as {\it quantitative frameproof codes and hypergraphs}. We give asymptotically optimal bounds on the maximum sizes of these structures and determine their exact sizes for a broad range of parameters. In particular, we introduce a generalized version of the Erdős matching number in our proof and derive relevant estimates for it.

math.CO↗

arXiv2025

Distinguishing Quantum and Classical Gravity via Non-Stationary Test Mass Dynamics

Classical gravity theory predicts a state-dependent gravitational potential for a quantum test mass, leading to nonlinear Schrodinger-Newton (SN) state evolution that contrasts with quantum gravity. Testing the effect of SN evolution can provide evidence for distinguishing quantum gravity and classical gravity, which is challenging to realize in the stationary optomechanical systems as analyzed in previous works [Phys. Rev. D 107, 024004 (2023), Phys. Rev. D 111, 062004 (2025)]. This work is devoted to analyzing the possibility of capturing the signature of SN theory during the non-stationary evolution of the test mass under the optomechanical measurement, where the second-order moments of a test mass can exhibit a distinctive oscillatory behavior. We show that this feature manifest in the non-stationary noise spectrum of outgoing light as additional peaks structures, although resolving these structures in practical experiments requires a larger number of repetitive trials with our sampling parameters, which is cost-prohibitive. To address this issue, we further employ statistical inference methods to extract more comprehensive information, thereby reducing the required number of experimental repetitions. Through Mock-Data simulations, we demonstrate that only 10 experimental trials of 40 seconds each are sufficient to reduce the false alarm rate for distinguishing between the two models to below one percent.

quant-ph↗

arXiv2025

Improved Bounds for Codes over Trees

Codes over trees were introduced recently to bridge graph theory and coding theory with diverse applications in computer science and beyond. A central challenge lies in determining the maximum number of labelled trees over $n$ nodes with pairwise distance at least $d$, denoted by $A(n,d)$, where the distance between any two labelled trees is the minimum number of edit edge operations in order to transform one tree to another. By various tools from graph theory and algebra, we show that when $n$ is large, $A(n,d)=O((Cn)^{n-d})$ for any $d\leq n-2$, and $A(n,d)=Ω((cn)^{n-d})$ for any $d$ linear with $n$, where constants $c\in(0,1)$ and $C\in [1/2,1)$ depending on $d$. Previously, only $A(n,d)=O(n^{n-d-1})$ for fixed $d$ and $A(n,d)=Ω(n^{n-2d})$ for $d\leq n/2$ were known, while the upper bound is improved for any $d$ and the lower bound is improved for $d\geq 2\sqrt{n}$. Further, for any fixed integer $k$, we prove the existence of codes of size $Ω(n^k)$ when $n-d=o(n)$, and give explicit constructions of codes which show $A(n,n-4)=Ω(n^2)$ and $A(n,n-13)=Ω(n^3)$.

math.CO↗

arXiv2024

Improvements on Permutation Reconstruction from Minors

We study the reconstruction problem of permutation sequences from their $k$-minors, which are subsequences of length $k$ with entries renumbered by $1,2,\ldots,k$ preserving order. We prove that the minimum number $k$ such that any permutation of length $n$ can be reconstructed from the multiset of its $k$-minors is between $\exp{(Ω(\sqrt{\ln n}))}$ and $O(\sqrt{n\ln n})$. These results imply better bounds of a well-studied parameter $N_d$, which is the smallest number such that any permutation of length $n\ge N_d$ can be reconstructed by its $(n-d)$-minors. The new bounds are $ d+\exp(Ω(\sqrt{\ln d}))<N_d<d+O(\sqrt{d\ln d})$ asymptotically, and the previous bounds were $d+\log_2 d<N_d<d^2/4+2d+4$.

math.CO↗

arXiv2024

Semiclassical gravity phenomenology under the causal-conditional quantum measurement prescription II: Heisenberg picture and apparent optical entanglement

The evolution of quantum states influenced by semiclassical gravity is distinct from that in quantum gravity theory due to the presence of a state-dependent gravitational potential. This state-dependent potential introduces nonlinearity into the state evolution, of which the theory is named Schroedinger-Newton (SN) theory. The formalism for understanding the continuous quantum measurement process on the quantum state in the context of semiclassical gravity theory has been previously discussed using the Schrödinger picture in Paper I [1]. In this work, an equivalent formalism using the Heisenberg picture is developed and applied to the analysis of two optomechanical experiment protocols that targeted testing the quantum nature of gravity. This Heisenberg picture formalism of the SN theory has the advantage of helping the investigation of the covariance matrices of the outgoing light fields in these protocols and further the entanglement features. We found that the classical gravity between the quantum trajectories of two mirrors under continuous quantum measurement in the SN theory can induce an apparent entanglement of the outgoing light field (though there is no quantum entanglement of the mirrors), which could serve as a false alarm for those experiments designed for probing the quantum gravity induced entanglement.

quant-ph↗

arXiv2024

Trace reconstruction of matrices and hypermatrices

A \emph{trace} of a sequence is generated by deleting each bit of the sequence independently with a fixed probability. The well-studied \emph{trace reconstruction} problem asks how many traces are required to reconstruct an unknown binary sequence with high probability. In this paper, we study the multivariate version of this problem for matrices and hypermatrices, where a trace is generated by deleting each row/column of the matrix or each slice of the hypermatrix independently with a constant probability. Previously, Krishnamurthy et al. showed that $\exp(\widetilde{O}(n^{d/(d+2)}))$ traces suffice to reconstruct any unknown $n\times n$ matrix (for $d=2$) and any unknown $n^{\times d}$ hypermatrix. By developing a dimension reduction procedure and establishing a multivariate version of the Littlewood-type result, we improve this upper bound by showing that $\exp(\widetilde{O}(n^{3/7}))$ traces suffice to reconstruct any unknown $n\times n$ matrix, and $\exp(\widetilde{O}(n^{3/5}))$ traces suffice to reconstruct any unknown $n^{\times d}$ hypermatrix. This breaks the tendency to trivial $\exp(O(n))$ as the dimension $d$ grows.

math.CO↗

arXiv2024

Reconstruction of hypermatrices from subhypermatrices

For a given $n$, what is the smallest number $k$ such that every sequence of length $n$ is determined by the multiset of all its $k$-subsequences? This is called the $k$-deck problem for sequence reconstruction, and has been generalized to the two-dimensional case -- reconstruction of $n\times n$-matrices from submatrices. Previous works show that the smallest $k$ is at most $O(n^\frac{1}{2})$ for sequences and at most $O(n^\frac{2}{3})$ for matrices. We study this $k$-deck problem for general dimension $d$ and prove that, the smallest $k$ is at most $O(n^\frac{d}{d+1})$ for reconstructing a $d$ dimensional hypermatrix of order $n$ from the multiset of all its subhypermatrices of order $k$.

math.CO↗

arXiv2023

Mass transfer and boson cloud depletion in a binary black hole system

Ultralight boson is one of the potential candidates for dark matter. If exists, it can be generated by a rapidly rotating black hole via superradiance, extracting the energy and angular momentum of the black hole and forming a boson cloud. The boson cloud can be affected by the presence of a companion star, generating fruitful dynamical effects and producing characteristic gravitational wave signals. We study the dynamics of the boson cloud in a binary black hole system, in particular, we develop a framework to study the mass transfer between two black holes. It is found that bosons occupying the growing modes of the central black hole can jump to the decaying modes of the companion black hole, resulting in cloud depletion. This mechanism of cloud depletion is different from that induced by the resonant perturbation from the companion.

gr-qc↗

arXiv2023

Comprehensive Solution Program Centric Pretraining for Table-and-Text Hybrid Numerical Reasoning

Numerical reasoning over table-and-text hybrid passages, such as financial reports, poses significant challenges and has numerous potential applications. Noise and irrelevant variables in the model input have been a hindrance to its performance. Additionally, coarse-grained supervision of the whole solution program has impeded the model's ability to learn the underlying numerical reasoning process. In this paper, we propose three pretraining tasks that operate at both the whole program and sub-program level: Variable Integrity Ranking, which guides the model to focus on useful variables; Variable Operator Prediction, which decomposes the supervision into fine-grained single operator prediction; and Variable Keyphrase Masking, which encourages the model to identify key evidence that sub-programs are derived from. Experimental results demonstrate the effectiveness of our proposed methods, surpassing transformer-based model baselines.

cs.CL↗

arXiv2020

Robust Automated Photometry Pipeline for Blurred Images

The primary task of the 1.26-m telescope jointly operated by the National Astronomical Observatory and Guangzhou University is photometric observations of the g, r, and i bands. A data processing pipeline system was set up with mature software packages, such as IRAF, SExtractor, and SCAMP, to process approximately 5 GB of observational data automatically every day. However, the success ratio was significantly reduced when processing blurred images owing to telescope tracking error; this, in turn, significantly constrained the output of the telescope. We propose a robust automated photometric pipeline (RAPP) software that can correctly process blurred images. Two key techniques are presented in detail: blurred star enhancement and robust image matching. A series of tests proved that RAPP not only achieves a photometric success ratio and precision comparable to those of IRAF but also significantly reduces the data processing load and improves the efficiency.

astro-ph.IM↗