论文标题
拉姆西理论通过多名应用于产品状态的本地化的应用
Application of Ramsey theory to localization of set of product states via multicopies
论文作者
论文摘要
众所周知，如果国家可以使用$（n-1）$副本，则始终在本地操作和经典通信（LOCC）下始终在本地操作和经典通信（LOCC）下进行完美区分任何众所周知。莱特牧师。 85，4972（2000）]。重要的是减少量子状态副本的数量，以确保从资源节省和非局部性强度表征的LOCC区分性。表示$ f_r（n）$ LOCC区分任何$ n $ orthoconal $ r $ r $ - 分段产品状态所需的最少副本。这项工作将用于估计$ f_r（n）$的上限。实际上，我们首先将这个问题与拉姆西理论（Ramsey Theory）联系起来，拉姆西理论（Ramsey Theory）是一个专门研究订单必须出现的条件的组合分支。随后，我们证明了$ f_2（n）\ leq \ lceil \ frac {n} {6} \ rceil+2 $，它比$ f_2（n）\ leq \ leq \ lceil \ frac {n} {4} {4} \ rceil $都更好。物理。 J. Plus 136，1172（2021）] $ N> 24 $。我们进一步表明，对于任意$ε> 0 $，$ f_r（n）\ leq \lceilεn\ rceil $总是适用于足够大的$ n $。
It is well known that any $N$ orthogonal pure states can always be perfectly distinguished under local operation and classical communications (LOCC) if $(N-1)$ copies of the state are available [Phys. Rev. Lett. 85, 4972 (2000)]. It is important to reduce the number of quantum state copies that ensures the LOCC distinguishability in terms of resource saving and nonlocality strength characterization. Denote $f_r(N)$ the least number of copies needed to LOCC distinguish any $N$ orthogonal $r$-partite product states. This work will be devoted to the estimation of the upper bound of $f_r(N)$. In fact, we first relate this problem with Ramsey theory, a branch of combinatorics dedicated to studying the conditions under which orders must appear. Subsequently, we prove $f_2(N)\leq \lceil\frac{N}{6}\rceil+2$, which is better than $f_2(N)\leq \lceil\frac{N}{4}\rceil$ obtained in [Eur. Phys. J. Plus 136, 1172 (2021)] when $N>24$. We further exhibit that for arbitrary $ε>0$, $f_r(N)\leq\lceilεN\rceil$ always holds for sufficiently large $N$.
