Comprehensive proof of the Greenberger-Horne-Zeilinger Theorem for the four-qubit system

Details Comprehensive proof of the Greenberger-Horne-Zeilinger Theorem for the four-qubit system Comprehensive proof of the Greenberger-Horne-Zeilinger Theorem for the four-qubit system

2005-09-22

arxiv.org/abs/quant-ph/0509158v1

Physics

Quantum Physics

14 pages

Scientific paper

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. In this paper, however, for a four-qubit system which was originally studied by GHZ, we show that there are nine distinct forms of the GHZ-Mermin-like argument. The proof is obtained by using some 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.

Affiliated with

Also associated with

No associations

Rating

Comprehensive proof of the Greenberger-Horne-Zeilinger Theorem for the four-qubit system does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Comprehensive proof of the Greenberger-Horne-Zeilinger Theorem for the four-qubit system, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Comprehensive proof of the Greenberger-Horne-Zeilinger Theorem for the four-qubit system will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-503944