发表机构
Leinweber Institute for Theoretical Physics, Stanford University; Department of Physics, Syracuse University; Institute for Quantum and Information Sciences, Syracuse University; Zyphra; QICI Quantum Information and Computation Initiative, School of Computing and Data Science, The University of Hong Kong（莱因韦伯理论物理研究所，斯坦福大学; 锡拉丘兹大学物理系; 锡拉丘兹大学量子与信息科学研究所; Zyphra; 香港大学计算与数据科学学院量子信息与计算倡议）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本研究探讨Schumacher压缩变体，针对已知谱和未知本征基的密度矩阵多副本，确定最小内存成本，通过加性常数、Werner克隆映射推广及Koashi--Imoto不可压缩性定量形式，并关联通用无损编码开销，提供Lean证书验证。
AI 中文摘要
我们研究Schumacher压缩的一个变体。该任务要求在已知谱和未知本征基的情况下，压缩密度矩阵的多个副本所需的最小内存成本，且不保留其纯化。对于固定维数和不同的正本征值，我们通过其加性常数获得该成本。可实现性使用了Werner克隆映射到$\mathrm{GL}(d,\mathbb C)$不可约表示的推广，并受最高权重差和行间隙控制的有限迹距离界。匹配的逆命题来自Koashi--Imoto不可压缩性在谱间隙假设下对不可约群轨道的定量形式。我们还确定了该量子最小描述长度与通用无损编码开销之间的关系，其与自由熵的联系在配套信件中说明。我们为我们的证明提供了Lean证书。
英文摘要
We study a variant of Schumacher compression. The task asks for the minimal memory cost for compressing many copies of a density matrix with known spectrum and unknown eigenbasis, without preserving its purification. For fixed dimension and distinct positive eigenvalues, we obtain the cost through its additive constant. Achievability uses a generalization of Werner's cloning map to $\mathrm{GL}(d,\mathbb C)$ irreducible representations, with finite trace-distance bounds controlled by highest-weight differences and row gaps. The matching converse follows from a quantitative form of Koashi--Imoto incompressibility for irreducible group orbits under a spectral-gap assumption. We also identify the relation between this quantum minimum description length and universal lossless coding overhead, and its connection to free entropy is explained in a companion letter. We provide a Lean certificate for our proofs.
Comments32pp; see also a concurrent letter; Lean certificate: https://github.com/JWang226/Quantum-Minimum-Description-Length
