arXiv subjects

Jing-Ling Chen

Publications and source records attributed to Jing-Ling Chen.

At least 19 recordsLinked to original sources

arXiv2026

Analytic Maximal Violation of Extended MABK Inequalities for Generalized GHZ States

We analytically characterize the maximal quantum violation of the extended Mermin-Ardehali-Belinskii-Klyshko (EMABK) family of inequalities by $n$-qubit generalized Greenberger-Horne-Zeilinger (GHZ) states. We develop a correlation-tensor approach in which the Bell value is expressed as the Frobenius inner product of the quantum correlation tensor and an effective coefficient tensor. A rank constraint on the latter, together with the von Neumann trace inequality, yields an upper bound governed by the two largest singular values of the reshaped correlation-tensor. For generalized GHZ states, we determine the complete singular spectrum and obtain a piecewise analytic upper bound. We then construct two complementary measurement strategies that saturate the bound for EMABK throughout the entire parameter range. The first is a purely MABK strategy in which all measurement directions lie in the equatorial plane of the Bloch sphere. The second is a hybrid strategy that recursively combines lower-order MABK anti-diagonal operators with the fully-$\sigma_z$ tensor product. The resulting piecewise analytic expression recovers the standard MABK Tsirelson bound $2^{(n-1)/2}$ in the maximally entangled limit and approaches the classical local-hidden-variable bound in the product-state limits. It further shows that every entangled generalized GHZ state exhibits a strict quantum-classical separation under the EMABK inequality, thereby eliminating the nonviolation region of the standard MABK inequality in the partially entangled regime.

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arXiv2026

Equality Conditions for an Additive Three-Observable Uncertainty Relation

Uncertainty relations play a fundamental role in quantum mechanics by quantifying the intrinsic limitations on the simultaneous sharpness of incompatible observables. Beyond the standard two-observable product form, additive uncertainty relations for triples of observables provide a natural framework for describing collective constraints among three noncommuting components. In this work, we study an additive uncertainty relation for three Hermitian observables from the viewpoint of rotational symmetry and covariance geometry. We give a short rotational derivation by rotating the observable triple and applying the Robertson uncertainty relation to the two transverse observables. This derivation makes the saturation mechanism transparent and leads to a necessary and sufficient condition for equality for general density operators. In the nontrivial equality case, the covariance ellipsoid of the observable triple degenerates into a disk perpendicular to the expectation value of the commutator vector. We also discuss an inverse construction based on finite-dimensional representations of the Lie algebra $\mathfrak{su}(2)$, which provides a systematic way to construct observable triples with prescribed saturating states. These results clarify the geometric and representation-theoretic structure underlying the tightness of additive three-observable uncertainty relations.

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arXiv2026

The Quantum Hamming Bound in Arbitrary Local Dimension

The quantum Hamming bound is the finite-length sphere-packing count for exact quantum error correction: the code dimension times the number of correctable local error patterns must fit inside the ambient Hilbert space. For nondegenerate codes this follows from disjoint error spheres. Degeneracy is the only obstruction, because distinct physical errors can coincide on the code subspace and turn sphere packing into an overcount. The central finite-length question has been whether this overcount can ever invalidate the Hamming inequality. Earlier linear-programming, asymptotic, and structural results left a pointwise finite-length problem for arbitrary exact subspace codes. Writing $Q=q^2$ for the Hamming-scheme alphabet, the nonbinary range begins at $Q=9$; here we prove the bound for every $q\ge3$, while the binary endpoint is governed by a distinct $Q=4$ charging geometry. For every nontrivial exact subspace code in this range, any possible violation reduces to a two-center Hamming-ball intersection inequality normalized by the Lloyd response. For $q\ge4$, the Lloyd-square linear program has a uniform half-gap after reduction to alphabet $Q\ge16$ and critical length $n=4t+1$. Qutrits form the boundary: the half-gap disappears, but the bridge is handled by a quadratic-filtered Lloyd square, an exact coefficient-certificate reduction, and a Stein-tangent positivity argument. Thus degeneracy may merge error sectors, but not enough to beat the Hamming count. This proves the nonbinary part of the finite-length quantum Hamming bound; together with the independent binary endpoint theorem, it gives the result in arbitrary local dimension.

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arXiv2026

Degeneracy Cannot Violate the Quantum Hamming Bound

The quantum Hamming bound is the standard finite-length sphere-packing bound for exact correction of arbitrary qubit errors. Whether degeneracy can evade this bound has remained unresolved in full generality for nearly three decades: distinct correctable errors may act identically on the code space, so the usual disjoint-sphere argument breaks down. We prove that every exact binary quantum subspace code with $K>1$ obeys the bound, without assuming either nondegeneracy or additivity. Our proof turns the Li--Xing linear-programming polynomial into an exact intersection count for quaternary Hamming balls. Monotonicity in block length and in ball-center separation then reduces the problem to a local node--edge charging inequality at the shortest admissible length. Thus degeneracy can merge correctable error sectors, but cannot enlarge the finite-length binary Hamming bound.

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arXiv2026

Every Rank-2 Bipartite Entangled State is Projectively Steerable

We prove that every rank-2 bipartite entangled state is already steerable with projective measurements, closing the first possible gap between entanglement and Einstein-Podolsky-Rosen (EPR) steering. In arbitrary finite local dimensions, any rank-2 entangled state is projectively steerable in at least one direction; when the effective dimensions are equal, steering is two-way. The argument is geometric: a rank obstruction forces some projective outcome on the larger local system to reach the boundary of the trusted-state space. From this boundary contact, a neighboring measurement produces a linear displacement that cannot be reproduced by a local-hidden-state model, because positivity only permits a quadratic filling into a kernel direction. This same block witnesses partial-transpose entanglement. If the contact is degenerate, a Schur complement removes one product layer and reduces the problem to a lower-rank entangled residual; each such reduction lowers the rank, so the recursion terminates. More broadly, we derive a directional rank criterion: if an $m\otimes n$ entangled state $\rho$ satisfies $\rank\rho\le 1+\lfloor(m-1)/(n-1)\rfloor$, then it is projectively steerable from $A$ to $B$. Since counterexamples already occur at rank three, rank two is the unique mixed rank for which entanglement guarantees projective steering, and the proof provides an operational certificate based solely on the support and kernel of the density matrix.

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arXiv2026

Boundary Geometry Turns Entanglement into Steering

Quantum entanglement does not necessarily imply Einstein-Podolsky-Rosen steering. We identify a \emph{boundary mechanism} that closes this gap when an entangled state meets the boundary of the trusted state space in a nondegenerate way. The mechanism is local: a projective assemblage that approaches a boundary contact with first-order tangential coherence but only second-order inward defect cannot be reproduced by any finite-measure local-hidden-state model. In finite dimensions this yields a support-kernel criterion for an arbitrary fixed steering cut: if a trusted conditional state is rank-deficient and its first-order block couples its support to its kernel, then the state is both NPT (negative partial transpose) and projectively steerable. The two-qubit product-null sector provides the minimal transparent realization. A product vector in the kernel gives the pure boundary contact, and a single coherence entry simultaneously serves as the tangential displacement, the NPT minor, and the steering obstruction. Hence, on this boundary, entanglement collapses to two-way projective steering -- including the genuinely mixed rank-three branch and the rank-two case as a low-dimensional instance. We also provide a filtered standard form, an explicit rank-three Cholesky parametrization, and a compact boundary certificate.

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arXiv2026

Systematic Extraction of Exact Yang-Mills Solutions via Algebraic Tensor Ring Decomposition

The non-linear nature of Yang-Mills theory presents a challenge for extracting exact classical solutions, which are useful for understanding non-perturbative vacuum structures. In this paper, an algebraic tensor ring decomposition framework is introduced to systematically map the non-linear partial differential equations (PDEs) of Yang-Mills theory into tractable differential-algebraic systems. By promoting static pure-gauge backgrounds to dynamical variables, the reference state acts as a geometric template whose Maurer-Cartan forms generate the algebraic cross-terms necessary to stabilize non-linear self-interactions. To analytically resolve the resulting differential ideals, specific differential-algebraic quotient rings are employed as evaluation tools, and the solution space is organized by an algebraic bifurcation analysis. Applying this framework, three distinct classes of exact solutions are extracted: (i) relativistic $SU(2)$ color waves evaluated over an elliptic quotient ring, where the differential ideal bifurcates into a Decoupled Branch and two Coupled Branches, the latter exhibiting mass gap generation; (ii) dynamical dyonic flux tubes obtained from a time-dependent helical template, where the Gauss law ideal bifurcates the system into Coulomb, Dyonic, and symmetric Meissner branches. In the Meissner branch, an Artinian asymptotic truncation yields Bessel-type exponential screening, stabilized by a temporal dominance condition; and (iii) dynamical $SU(3)$ configurations where the Gauss law ideal bifurcates the solution space into four distinct phases. The non-trivial branches enforce a kinetic cancellation mechanism that maps the amplitude dynamics onto a generalized $x^2y^2$ chaotic oscillator. Across these settings, the framework provides a methodical approach to characterize the classical solution space of strongly coupled gauge theories.

hep-th↗

arXiv2026

Exact SU(2) Yang-Mills Waves from a Simple Ansatz

We propose a simple ansatz that reduces the sourceless SU(2) Yang--Mills equations in (3+1) dimensions to nine algebraic constraints. Solving these constraints yields three closed-form families of exact wave solutions. \textbf{Family I} embeds linear electromagnetic waves into the non-Abelian theory, with vanishing commutators and dispersion $\omega = kc$. \textbf{Family II} describes genuinely nonlinear self-interacting waves that also propagate at the speed of light but exhibit a constant, gauge-invariant offset in the color-electric field, nonvanishing commutators, and a discrete topological parameter $\xi\eta = \pm 1$ that controls the position of energy-density nodes ($\theta=0$ or $\theta=\pi$). This provides an observable signature with no analogue in Abelian electromagnetism. \textbf{Family III} is a pure gauge solution with vanishing field strengths, valid for arbitrary $k$ and $\omega$ without any dispersion relation. These exact solutions offer new insights into how non-Abelian self-interactions fundamentally alter wave propagation and serve as benchmarks for numerical simulations, perturbative studies, and experiments on synthetic non-Abelian gauge fields.

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arXiv2026

Exact Solutions of the SU(2) Yang-Mills Equations from a Static Ansatz

We present a systematic study of static solutions to the source-free SU(2) Yang-Mills equations, in which the gauge potential explicitly depends on spin operators. By employing the \emph{vector potential extraction approach} -- which requires the total angular momentum operator (orbital plus spin) to satisfy the standard angular momentum algebra -- we derive the most general form of the spin vector potential $\vec{A}$. This leads to the static ansatz $\{ \vec{A} = [k_1(\hat{r}\times\vec{\Gamma}) + k_2\vec{\Gamma} + k_3(\vec{\Gamma}\cdot\hat{r})\hat{r}]/r, \varphi = f_1(r)\,(\vec{\Gamma}\cdot\hat{r}) + f_2(r)\}$, parametrized by three constants $\{k_1, k_2, k_3\}$ and two radial functions $\{f_1(r), f_2(r)\}$. After substituting this static ansatz into the Yang-Mills equations we obtain a set of consistency equations. Solving these equations provides a complete classification of the exact static solutions, including both real and complex families. The known simple SU(2) static solution $\{\vec{A}=\tilde{k} (\hat{r}\times\vec{\Gamma})/r, \varphi=\kappa/r \}$ is recovered as a special case. Our classification reveals new static configurations that could be valuable for non-perturbative studies and for models where the internal spin couples to non-Abelian gauge fields.

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arXiv2026

Peres-type Criterion of Einstein-Podolsky-Rosen Steering for Two Qubits

Quantum nonlocality manifests in multipartite systems through entanglement, Bell's nonlocality, and Einstein-Podolsky-Rosen (EPR) steering. While Peres's positive-partial-transpose criterion provides a simple and powerful test for entanglement, a comparably elegant spectral criterion for detecting EPR steering remains an open challenge. In this work, we systematically explore whether a Peres-type criterion can be established for EPR steering in the two-qubit system. Focusing on rank-2 (including rank-1) states and the two-qubit Werner state, we analyze the eigenvalues of their partially transposed density matrices and construct a significant steering criterion based on symmetric combinations of these eigenvalues. We prove that this criterion serves as a necessary and sufficient condition for steerability for the Werner state, all two-qubit pure states, all two-qubit rank-2 states. Furthermore, we validate the criterion for higher-rank states (rank-3 and rank-4) and show that the results align with known steering inequalities. Our findings suggest a more unified framework for detecting quantum nonlocality via partial transposition and open avenues for further theoretical and numerical investigations into steering detection.

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arXiv2025

Steerability of Rank-2 Two-Qubit Entangled States

Quantum nonlocality is an essential resource in quantum information and is commonly classified into three distinct forms: quantum entanglement, Einstein-Podolsky-Rosen (EPR) steering, and Bell's nonlocality. Gisin's theorem shows that pure-state entanglement implies Bell nonlocality, and it motivates the question of how entanglement and EPR steering are related beyond pure states. Here we prove that every entangled rank-2 two-qubit state is EPR steerable, with rank-1 states included as a special case. The proof combines a local-unitary parametrization of rank-2 two-qubit states, a necessary and sufficient separability condition, and a state-dependent nonlinear steering inequality. This gives an analytical characterization of EPR steerability for rank-2 two-qubit entangled states. Thus, rank-2 two-qubit entangled states provide certifiable EPR-steering resources in quantum information.

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arXiv2025

Identifying the $3$-qubit $W$ state with quantum uncertainty relation

The $W$ state, a canonical representative of multipartite quantum entanglement, plays a crucial role in quantum information science due to its robust entanglement properties. Quantum uncertainty relations, on the other hand, are a fundamental cornerstone of quantum mechanics. This paper introduces a novel approach to Identifying tripartite $W$ states by leveraging tripartite quantum uncertainty relations. By employing a specific set of non-commuting observables, we formulate an uncertainty-based criterion for identifying $W$ states and rigorously demonstrate its generality in distinguishing them from other tripartite entangled states, such as the Greenberger-Horne-Zeilinger state. Our approach bypasses the need for complete quantum state tomography, as it requires only the verification of a set of uncertainty inequalities for efficient $W$-state identification. This work provides a new theoretical tool for identifying multipartite entangled states and underscores the significant role of quantum uncertainty relations in entanglement characterization.

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arXiv2025

Exploring the boundary of quantum correlations with a time-domain optical processor

Contextuality is a hallmark feature of the quantum theory that captures its incompatibility with any noncontextual hidden-variable model. The Greenberger--Horne--Zeilinger (GHZ)-type paradoxes are proofs of contextuality that reveal this incompatibility with deterministic logical arguments. However, the GHZ-type paradox whose events can be included in the fewest contexts and which brings the strongest nonclassicality remains elusive. Here, we derive a GHZ-type paradox with a context-cover number of three and show this number saturates the lower bound posed by quantum theory. We demonstrate the paradox with a time-domain fiber optical platform and recover the quantum prediction in a 37-dimensional setup based on high-speed modulation, convolution, and homodyne detection of time-multiplexed pulsed coherent light. By proposing and studying a strong form of contextuality in high-dimensional Hilbert space, our results pave the way for the exploration of exotic quantum correlations with time-multiplexed optical systems.

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arXiv2025

Quantum information masking basing on quantum teleportation

The no-masking theorem says that masking quantum information is impossible in a bipartite scenario. However, there exist schemes to mask quantum states in multipartite systems. In this work, we show that, the joint measurement in the teleportation is really a masking process, when the apparatus is regarded as a quantum participant in the whole system. Based on the view, we present two four-partite maskers and a tripartite masker. One of the former provides a generalization in arbitrary dimension of the four-qubit scheme given by Li and Wang [Phys. Rev. A 98, 062306 (2018)], and the latter is precisely their tripartite scheme. The occupation probabilities and coherence of quantum states are masked in two steps of our schemes. And the information can be extracted naturally in their reverse processes.

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arXiv2025

Exactly Solvable Quantum Model with Spin-Dependent Coulomb Interaction

In this work, we report an exactly solvable quantum model featuring a spin-dependent Coulomb interaction, described by the spin vector potential $\vec{\mathcal{A}} = k (\vec{r} \times \vec{S}) / r^2$ together with a Coulomb-type scalar potential $\varphi = \kappa / r$ . The model is governed by the Schr\"odinger-type Hamiltonian $\mathcal{H}_{\rm S} = \vec{\Pi}^2 / (2M) + q \varphi$ in nonrelativistic quantum mechanics and by the Dirac-type Hamiltonian $\mathcal{H}_{\rm D} = c \vec{\alpha} \cdot \vec{\Pi} + \beta M c^2 + q \varphi$ in relativistic quantum mechanics, where $\vec{\Pi} = \vec{p} - (q/c)\vec{\mathcal{A}}$ is the canonical momentum. We demonstrate two main results: (i) Just as the Coulomb-type scalar potential $\mathcal{S}_{\rm Maxwell} = \{\vec{\mathcal{A}} = 0,\ \varphi = \kappa / r\}$ is a local exact solution of Maxwell's equations on $r\neq0$, the gauge potential $\mathcal{S}_{\rm YM} = \{\vec{\mathcal{A}} = k (\vec{r} \times \vec{S}) / r^2,\ \varphi = \kappa / r\}$ constitutes a local exact solution of the Yang--Mills equations on the punctured region $r\neq0$. (ii) Both Hamiltonians $\mathcal{H}_{\rm S}$ and $\mathcal{H}_{\rm D}$ can be solved exactly in the presence of this spin-dependent Coulomb interaction. The resulting energy spectra are derived, and they naturally reduce to those of the ordinary hydrogen atom when the spin-dependent terms are neglected. Finally, we clarify the quantization conditions and the fixed-background interpretation of the model.

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arXiv2025

Electric-Type Stern-Gerlach Effect

The Stern-Gerlach (SG) experiment is a fundamental experiment for revealing the existence of ``spin''. In such an experiment, beams of silver atoms were sent through inhomogeneous magnetic fields to observe their deflection. Thus, the conventional SG experiment can be actually viewed as a magnetic-type spin effect. In this work, we successfully generalize the SG effect from magnetic-type to electric-type by solving Dirac's equation with a potential barrier, thus revealing an extraordinary spin effect. Beams of Dirac's particles can be regarded as matter waves. Based on Dirac's equation, we obtain the explicit forms of the incident, reflected, and transmitted waves. The electric-type SG effect shows that the reflected and transmitted waves can have notable spatial shifts, which depend on the spin direction and the incident angle of incident wave. The electric-type SG effect has potential applications to separating Dirac's particles with different spin directions and to estimating the spin direction of Dirac's particles. Some discussions related to the interaction between spin and electric field are also made.

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arXiv2024

Entanglement measurement based on convex hull properties

Quantum entanglement is a unique correlation phenomenon in quantum mechanics, and the measurement of quantum entanglement plays an important role in quantum computing and quantum communication. Many mainstream entanglement criteria and measurement methods currently known have shortcomings in certain aspects, such as not being sufficient or necessary conditions for entanglement, or only being effective in simple cases such as 2-qubits or pure states. In this work, we will propose a scheme for measuring quantum entanglement, which starts with treating the set of quantum separable states as a convex hull of quantum separable pure states, and analyzes the properties of the convex hull to obtain a new form of entanglement measurement. Although a large amount of data is required in the measurement process, this method is not only applicable to 2-qubit quantum states, but also a entanglement measurement method that can be applied to any dimension and any fragment. We will provide several examples to compare their results with other entanglement metrics and entanglement determination methods to verify their feasibility.

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arXiv2024

Observing tight triple uncertainty relations in two-qubit systems

As the fundamental tool in quantum information science, the uncertainty principle is essential for manifesting nonclassical properties of quantum systems. Plenty of efforts on the uncertainty principle with two observables have been achieved, making it an appealing challenge to extend the scenario to multiple observables. Here, based on an optical setup, we demonstrate the uncertainty relations in two-qubit systems involving three physical components with the tight constant $2/\sqrt{3}$, which signifies a more precise limit in the measurement of multiple quantum components and offers deeper insights into the trade-offs between observables. Furthermore, we reveal the correspondence of the maximal values of the uncertainty functions and the degree of entanglement, where the more uncertainty is proportional to the higher degree of entanglement. Our results provide a new insight into understanding the uncertainty relations with multiple observables and may motivate more innovative applications in quantum information science.

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