Brauer态的可扩展性
Extendibility of Brauer states
AI总结：
该研究通过表示论方法确定了Brauer态的(n,m)-可扩展性和n-de Finetti-可扩展性条件，并揭示了其在n和m之间的非平凡权衡。
摘要：
我们研究Brauer态的可扩展性问题，重点探讨对称的双侧可扩展性和de Finetti可扩展性。通过运用单位ary和正交群的表示论，我们提供了一种通用的配方，用于确定(n,m)-可扩展和n-de Finetti-可扩展的Brauer态集合。从对角作用于正交群的交换子的具体形式出发，我们明确确定了Brauer态在任意维度d下为(1,2)、(1,3)和(2,2)-可扩展的参数集合，并发现Brauer态在n和m之间存在非平凡的权衡。利用相同的配方，我们还提供了任意m和维度d下(1,m)-可扩展的Brauer态集合的估计。最后，利用从U(d)到O(d)的分支规则，我们获得了任意维度下n-de Finetti-可扩展的Brauer态集合，并且分析地描述了n→∞时的极限形状，结果发现对于奇数维并非多边形。
英文摘要：
We investigate the extendibility problem for Brauer states, focusing on the symmetric two-sided extendibility and the de Finetti extendibility. By employing the representation theory of the unitary and orthogonal groups, we provide a general recipe for determining the set of $(n,m)$-extendible and $n$-de Finetti-extendible Brauer states. From the concrete form of the commutant of the diagonal action of the orthogonal group, we explicitly determine the set of parameters for which the Brauer states are $(1,2)$-, $(1,3)$- and $(2,2)$-extendible in any dimension $d$ and find that Brauer states extend with a non-trivial trade-off in $n$ and $m$. Using the same recipe we also provide an estimate of the set of $(1,m)$-extendible Brauer states for any $m$ and dimension $d$. Finally, using the branching rules from $\mathrm{U}(d)$ to $\mathrm{O}(d)$, we obtain the set of $n$-de Finetti-extendible Brauer states in any dimension, and also analytically describe the $n\to\infty$ limiting shape which turns out not to be a polygon for odd dimensions.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
