arXiv subjects

Zhixiang Jin

Publications and source records attributed to Zhixiang Jin.

4 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↗

arXiv2025

Measure of entanglement and the monogamy relation: a topical review

Characterizing entanglement, including quantifying and distribution of entanglement, which lies at heart of the quantum resource theory, have been investigated extensively ever since Bennett \etal proposed three seminal measures of entanglement in 1996. Up to now, there are numerous measures of entanglement that have been proposed from different point of view and plenty of monogamy relations have been explored which make the distribution of entanglement became more and more clear. While this is relatively easy in the case of pure states, it is much more intricate for the case of mixed quantum states especially with higher dimension and more particles in the system. We present here an overview of the theory along this line. We outline most of the results in this field historically and focus on the finite-dimensional systems. In particular we emphasize the point of view that (i) which yardsticks haven been applied in quantifying entanglement and its distribution, (ii) what are the substantive characteristics and interrelations of these measures and their monogamy relations mathematically by comparing, and (iii) which concepts should be improved or revised and how they were developed accordingly.

quant-ph↗

arXiv2024

Differentiable Information Bottleneck for Deterministic Multi-view Clustering

In recent several years, the information bottleneck (IB) principle provides an information-theoretic framework for deep multi-view clustering (MVC) by compressing multi-view observations while preserving the relevant information of multiple views. Although existing IB-based deep MVC methods have achieved huge success, they rely on variational approximation and distribution assumption to estimate the lower bound of mutual information, which is a notoriously hard and impractical problem in high-dimensional multi-view spaces. In this work, we propose a new differentiable information bottleneck (DIB) method, which provides a deterministic and analytical MVC solution by fitting the mutual information without the necessity of variational approximation. Specifically, we first propose to directly fit the mutual information of high-dimensional spaces by leveraging normalized kernel Gram matrix, which does not require any auxiliary neural estimator to estimate the lower bound of mutual information. Then, based on the new mutual information measurement, a deterministic multi-view neural network with analytical gradients is explicitly trained to parameterize IB principle, which derives a deterministic compression of input variables from different views. Finally, a triplet consistency discovery mechanism is devised, which is capable of mining the feature consistency, cluster consistency and joint consistency based on the deterministic and compact representations. Extensive experimental results show the superiority of our DIB method on 6 benchmarks compared with 13 state-of-the-art baselines.

cs.IT↗

arXiv2019

Polygamy Inequalities for Qubit Systems

Entanglement polygamy, like entanglement monogamy, is a fundamental property of multipartite quantum states. We investigate the polygamy relations related to the concurrence $C$ and the entanglement of formation $E$ for general $n$-qubit states. We extend the results in [Phys. Rev. A 90, 024304 (2014)] from the parameter region $α\leq0$ to $α\leqα_0$, where $0<α_0\leq2$ for $C$, and $0<α_0\leq\sqrt{2}$ for $E$.

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