arXiv subjects

Nung-sing Sze

Publications and source records attributed to Nung-sing Sze.

3 recordsLinked to original sources

arXiv2026

Multiscale Schmidt-Spectrum Bounds for High-Dimensional Entanglement: Geometric Measures and Schmidt-Number Witnesses

High-dimensional bipartite entanglement depends on how probability is distributed across the Schmidt spectrum, whereas a single reference-state fidelity resolves only one spectral scale. We develop multiscale Schmidt-spectrum bounds that connect geometric measures with quantitative Schmidt-number witnesses. For any partition of a pure-state Schmidt spectrum, several nested Vidal tails determine block masses. We derive the sharp upper boundary of the associated normalized nuclear-norm coordinate and show that equality holds if and only if the spectrum is uniform within each block. Refining the partition gives a monotone hierarchy of tighter bounds whenever the added tail data distinguish unequal block means. We also solve a relaxed weighted multiscale optimization globally: one scalar parameter specifies its unique full-support optimizer and explicit value on the nontrivial branch. Using the established single-tail fidelity--resource curve as a baseline, we obtain exact-fidelity equality refinements, convex-roof lower bounds for mixed states, and quantitative calibrations of Schmidt-number witnesses. A higher-tail relation further bounds convex-roof extended negativity in terms of Vidal tails and identifies the pure-state equality spectra. Leakage-aware and joint-confidence formulations state how these bounds can be used with incomplete data. Multistep tails require block-resolved or independently certified spectral information; they are not determined by one projector expectation.

quant-ph↗

arXiv2026

A smoothing moving balls approximation method for a class of conic-constrained difference-of-convex optimization problems

In this paper, we consider the problem of minimizing a difference-of-convex objective over a nonlinear conic constraint, where the cone is closed, convex, pointed and has a nonempty interior. We assume that the support function of a compact base of the polar cone exhibits a majorizing smoothing approximation, a condition that is satisfied by widely studied cones such as $\mathbb{R}^m_-$ and ${\cal S}^m_-$. Leveraging this condition, we reformulate the conic constraint equivalently as a single constraint involving the aforementioned support function, and adapt the moving balls approximation (MBA) method for its solution. In essence, in each iteration of our algorithm, we approximate the support function by a smooth approximation function and apply one MBA step. The subproblems that arise in our algorithm always involve only one single inequality constraint, and can thus be solved efficiently via one-dimensional root-finding procedures. We design explicit rules to evolve the smooth approximation functions from iteration to iteration and establish the corresponding iteration complexity for obtaining an $(ε_1, ε_2, ε_1 \sqrt{ε_2})$-Karush-Kuhn-Tucker point. In addition, in the convex setting, we establish convergence of the sequence generated, and study its local convergence rate under a standard Hölderian growth condition. Finally, we perform numerical experiments to illustrate the performance of our algorithm.

math.OC↗

arXiv2025

Characterizing High Schmidt Number Witnesses in Arbitrary Dimensions System

A profound comprehension of quantum entanglement is crucial for the progression of quantum technologies. The degree of entanglement can be assessed by enumerating the entangled degrees of freedom, leading to the determination of a parameter known as the Schmidt number. In this paper, we develop an efficient analytical tool for characterizing high Schmidt number witnesses for bipartite quantum states in arbitrary dimensions. Our methods not only offer viable mathematical methods for constructing high-dimensional Schmidt number witnesses in theory but also simplify the quantification of entanglement and dimensionality. Most notably, we develop high-dimensional Schmidt number witnesses within arbitrary-dimensional systems, with our Schmidt witness coefficients relying solely on the operator Schmidt coefficient. Subsequently, we demonstrate our theoretical advancements and computational superiority by constructing Schmidt number witnesses in arbitrary dimensional bipartite quantum systems with Schmidt numbers four and five.

quant-ph↗