Any multipartite entangled state violating the Mermin-Klyshko inequality can be distilled for almost all bipartite splits
- Authors
- Lee, Soojoon; Lee, Jinhyoung; Kim, Jaewan
- Issue Date
- Mar-2009
- Publisher
- AMER PHYSICAL SOC
- Keywords
- Bell theorem; bound states; quantum computing; quantum entanglement
- Citation
- PHYSICAL REVIEW A, v.79, no.3, pp.1 - 4
- Indexed
- SCIE
SCOPUS
- Journal Title
- PHYSICAL REVIEW A
- Volume
- 79
- Number
- 3
- Start Page
- 1
- End Page
- 4
- URI
- https://scholarworks.bwise.kr/hanyang/handle/2021.sw.hanyang/177150
- DOI
- 10.1103/PhysRevA.79.032309
- ISSN
- 1050-2947
- Abstract
- We study the explicit relation between violation of Bell inequalities and bipartite distillability of multiqubit states. It has been shown that even though for N >= 8 there exist N-qubit bound entangled states which violates a Bell inequality [W. Dur, Rev. Lett. 87, 230402 (2001)], for all the states violating the inequality there exists at least one splitting of the parties into two groups such that pure-state entanglement can be distilled [A. Acin, Rev. Lett. 88, 027901 (2002)]. We here prove that for all N-qubit states violating the inequality the number of distillable bipartite splits increases exponentially with N, and hence the probability that a randomly chosen bipartite split is distillable approaches 1 exponentially with N, as N tends to infinity. We also show that there exists at least one N-qubit bound entangled state violating the inequality if and only if N >= 6.
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