标题： 随机诱导态的绝对正部分转置性质 显示英文标题

标题： The absolute positive partial transpose property for random induced states

摘要： 在本文中，我们首先得到了中心Wishart矩阵矩的代数公式，并将其应用于当分布的两个参数以不同速度趋于无穷大时的大维极限下的新收敛结果。 我们利用这一结果来研究APPT（绝对正偏转）量子态。 我们证明，当环境维数$s$为$s_0=\min(d_1, d_2)^3 \max(d_1, d_2)$的数量级时，在$\C^d=\C^{d_1} \otimes \C^{d_2}$上由部分跟踪$\C^d \otimes \C^s$上的随机纯态得到的双部分随机诱导态是APPT的阈值出现。 也就是说，当$s \geq Cs_0$时，这样的随机诱导态以高概率是APPT的，而当$s \leq cs_0 $时，这样的随机态以高概率不是APPT的。 此外，我们有效地计算了$C$和$c$并表明当$\min(d_1, d_2)^{2}\ll d$时可以将它们替换为相同的尖锐跃迁常数。 显示英文摘要

摘要： In this paper, we first obtain an algebraic formula for the moments of a centered Wishart matrix, and apply it to obtain new convergence results in the large dimension limit when both parameters of the distribution tend to infinity at different speeds. We use this result to investigate APPT (absolute positive partial transpose) quantum states. We show that the threshold for a bipartite random induced state on $\C^d=\C^{d_1} \otimes \C^{d_2}$, obtained by partial tracing a random pure state on $\C^d \otimes \C^s$, being APPT occurs if the environmental dimension $s$ is of order $s_0=\min(d_1, d_2)^3 \max(d_1, d_2)$. That is, when $s \geq Cs_0$, such a random induced state is APPT with large probability, while such a random states is not APPT with large probability when $s \leq cs_0 $. Besides, we compute effectively $C$ and $c$ and show that it is possible to replace them by the same sharp transition constant when $\min(d_1, d_2)^{2}\ll d$.