arXivDaily arXiv每日学术速递 周一至周五更新
arXiv周末暂无论文更新，休息一下吧，周末愉快~~
arXiv 1412.4010quant-phmath.FAmath.PR
收藏

高概率抽样量子非定域关联

Sampling quantum nonlocal correlations with high probability

Carlos E. González-Guillén, C. Hugo Jiménez, Carlos Palazuelos, Ignacio Villanueva

备注：
v2: minor modifications to match the journal version, 16 pages, 0 figures
发表信息：
Commun. Math. Phys. (2016) 344: 141
阅读 PDF
arXiv 页面 ↗HTML 原文 ↗

摘要：

众所周知，二分二分测量的量子关联是$γ=(\langle u_i,v_j\rangle)_{i,j=1}^n$形式的量子关联，其中矢量$u_i$和$v_j$在实希尔伯特空间的单位球中。在这项工作中，我们研究了这些相关性的非局部性质的概率作为$α=\frac{m}{n}$的函数，其中以前的矢量根据Haar测量采样在单位球的$\mathbb R^m$。特别是，我们证明了存在的$α_0>0$，如果$α\leq α_0$，$γ$是非本地的概率倾向于$1$作为$n\rightarrow \infty$，而对于$α> 2$，$γ$是本地的概率倾向于$1$作为$n\rightarrow \infty$。

英文摘要：

It is well known that quantum correlations for bipartite dichotomic measurements are those of the form $γ=(\langle u_i,v_j\rangle)_{i,j=1}^n$, where the vectors $u_i$ and $v_j$ are in the unit ball of a real Hilbert space. In this work we study the probability of the nonlocal nature of these correlations as a function of $α=\frac{m}{n}$, where the previous vectors are sampled according to the Haar measure in the unit sphere of $\mathbb R^m$. In particular, we prove the existence of an $α_0>0$ such that if $α\leq α_0$, $γ$ is nonlocal with probability tending to $1$ as $n\rightarrow \infty$, while for $α> 2$, $γ$ is local with probability tending to $1$ as $n\rightarrow \infty$.

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。

↑