Application of Ramsey theory to localization of set of product states via multicopies
| Autor: | Guo, Xing-Chen, Li, Mao-Sheng |
|---|---|
| Rok vydání: | 2022 |
| Předmět: | |
| Zdroj: | Eur. Phys. J. Plus (2023) 138:50 |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1140/epjp/s13360-023-03656-4 |
| Popis: | 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 $\epsilon>0$, $f_r(N)\leq\lceil\epsilon N\rceil$ always holds for sufficiently large $N$. Comment: 13 pages |
| Databáze: | arXiv |
| Externí odkaz: |
|