唐莉; 陈泽乾; 钟杰; 任耀峰; 詹明生
Tang Li; Chen Zeqian; Zhong Jie; Ren Yaofeng; Zhan Mingsheng
摘要:
Greenberger--Horne--Zeilinger (GHZ) theorem asserts that there is a
set of mutually commuting nonlocal observables with a common
eigenstate on which those observables assume values that refute
the attempt to assign values only required to have them by the
local realism of Einstein, Podolsky, and Rosen (EPR). It is known
that for a three-qubit system, there is only one form of the
GHZ-Mermin-like argument with equivalence up to a local unitary
transformation, which is exactly Mermin's version of the GHZ
theorem. This article for a four-qubit system, which was originally studied by GHZ, the authors show that there are nine distinct forms of the GHZ-Mermin-like argument. The proof is obtained using certain geometric invariants to characterize the sets of mutually commuting nonlocal spin observables on the four-qubit system. It is proved that there are at most nine elements (except
for a different sign) in a set of mutually commuting nonlocal spin observables in the four-qubit system, and each GHZ-Mermin-like argument involves a set of at least five mutually commuting four-qubit nonlocal spin observables with a GHZ state as a common eigenstate in GHZ's theorem. Therefore, we present a complete construction of the GHZ theorem for the four-qubit system.
中图分类号: