Convex optimization on moment polytopes: Hadamard mirror descent and efficient algorithms for quantum functionals and other tensor parameters
本文针对难以处理的矩多面体上的凸优化问题，提出了Hadamard镜像下降法，有效解决了量子函数等张量参数的计算难题。
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Deterministic Identification over Additive Gaussian Channels
本文通过引入格理论的新视角，为加性高斯信道确定性识别容量提供紧致界，解决其容量未知的问题。
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The entanglement-assisted transmission capacity is a strong converse bound for identification
This study investigates the fundamental limits of classical identification over quantum channels, with a focus on the relationship between identification capacity and transmission capacity in the presence of entanglement assistance. By integrating Hayden–Winter quantum identification codes, the entanglement-assisted communication model, and an analysis of the transpose depolarizing channel, the work establishes—for the first time—that the entanglement-assisted transmission capacity serves as a strong converse upper bound on the identification capacity. The main contributions include precisely characterizing the identification capacity as achieving this bound in the low-noise regime, constructing an explicit family of channels for which the identification capacity is strictly smaller than the bound in general, and uncovering the first known instance of strict superadditivity of identification capacity.
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Multi-agent Autoformalization of Tensor Network Theory
This work addresses the lack of formal verification for foundational results in tensor network theory—such as the fundamental theorem of matrix product states—and the challenge of preserving mathematical intent during large-scale autoformalization. To this end, it introduces the first multi-agent collaborative framework for the automatic formalization of complex physical theories. Built upon the Lean theorem prover, the framework integrates domain-specialized large language model agents, structured mathematical blueprints, and a human-in-the-loop review mechanism. It successfully formalizes the fundamental theorem of matrix product states, uncovers a novel proof pathway absent from the literature, and extends formalization to physical concepts like symmetry-protected topological phases. The project also establishes TNLean, the first library for tensor networks and quantum information in Mathlib, with all code and formalization blueprints publicly released.
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Convex optimization on moment polytopes: Hadamard mirror descent and efficient algorithms for quantum functionals and other tensor parameters
本文针对难以处理的矩多面体上的凸优化问题，提出了Hadamard镜像下降法，有效解决了量子函数等张量参数的计算难题。
0 citationsRead paper
Deterministic Identification over Additive Gaussian Channels
本文通过引入格理论的新视角，为加性高斯信道确定性识别容量提供紧致界，解决其容量未知的问题。
0 citationsRead paper
The entanglement-assisted transmission capacity is a strong converse bound for identification
This study investigates the fundamental limits of classical identification over quantum channels, with a focus on the relationship between identification capacity and transmission capacity in the presence of entanglement assistance. By integrating Hayden–Winter quantum identification codes, the entanglement-assisted communication model, and an analysis of the transpose depolarizing channel, the work establishes—for the first time—that the entanglement-assisted transmission capacity serves as a strong converse upper bound on the identification capacity. The main contributions include precisely characterizing the identification capacity as achieving this bound in the low-noise regime, constructing an explicit family of channels for which the identification capacity is strictly smaller than the bound in general, and uncovering the first known instance of strict superadditivity of identification capacity.
0 citationsRead paper
Multi-agent Autoformalization of Tensor Network Theory
This work addresses the lack of formal verification for foundational results in tensor network theory—such as the fundamental theorem of matrix product states—and the challenge of preserving mathematical intent during large-scale autoformalization. To this end, it introduces the first multi-agent collaborative framework for the automatic formalization of complex physical theories. Built upon the Lean theorem prover, the framework integrates domain-specialized large language model agents, structured mathematical blueprints, and a human-in-the-loop review mechanism. It successfully formalizes the fundamental theorem of matrix product states, uncovers a novel proof pathway absent from the literature, and extends formalization to physical concepts like symmetry-protected topological phases. The project also establishes TNLean, the first library for tensor networks and quantum information in Mathlib, with all code and formalization blueprints publicly released.
0 citationsRead paper