添加或移除杨图方框的信道的最小输出熵，以及每个置换对称性的泡利原理
Minimal output entropy for the channels that add or remove a box of a Young diagram, and a Pauli principle for every permutation symmetry
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中文总结 AI 辅助
研究杨图相差一个方框的四个协变量子信道，证明相干态最小化输出熵并给出显式结果，应用于置换对称粒子的单粒子谱界，推广了泡利原理。
中文摘要 AI 辅助
两个杨图相差一个方框的 $U(d)$ 的不可约表示由四个协变量子信道连接：方框可以被移除或添加，并且保留新图或方框（$\mathbb{C}^d$ 或其对偶）。我们证明对于这些信道中的每一个，相干态的输出优超所有其他输出，因此相干态最小化输出熵，并且我们显式地用钩长计算最优输出。对于保留方框的两个信道，我们还确定了所有最小化器；这些最小化器不必是相干的，即使它们是纯态。作为应用，我们考虑具有给定置换对称性的 $N$ 个粒子，并找到单粒子约化密度矩阵谱的尖锐界，以及混合态可以达到的精确谱集（对于费米子，这些是泡利原理和科尔曼定理）。
英文摘要
Two irreducible representations of $U(d)$ whose Young diagrams differ by a single box are connected by four covariant quantum channels: the box can be removed or added, and one keeps either the new diagram or the box ($\mathbb{C}^d$ or its dual). We prove that for each of these channels the output of a coherent state majorizes every other output, so that coherent states minimize the output entropy, and we compute the optimal output explicitly in terms of hook lengths. For the two channels that keep the box we also determine all minimizers; these need not be coherent, even when they are pure. As an application we consider $N$ particles with a given permutation symmetry and find sharp bounds on the spectrum of the reduced density matrix of a single particle, as well as the exact set of spectra that mixed states can reach (for fermions these are the Pauli principle and Coleman's theorem).
发表机构
- Università degli Studi Roma Tre（罗马第三大学）
机构由 AI 辅助整理，请以论文原文为准。
