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 va...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 witha 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.展开更多
We propose a new multiparty simultaneous quantum direct communication scheme based on Creen-Horne- Zeilinger （CHZ） states and dense coding. For achieving high efficiency without leaking any information, four encodin...We propose a new multiparty simultaneous quantum direct communication scheme based on Creen-Horne- Zeilinger （CHZ） states and dense coding. For achieving high efficiency without leaking any information, four encoding schemes are prepared in advance. The present scheme has the capacity of transmitting （M ＋ 1）M classical bits per group of M-particle CHZ states when there exist M parties. The technique of rearranging particles makes the legal users coequally exchange their messages in the same length. Both high efficiency and excellent security against the common attacks are virtues of this new scheme.展开更多
基金Supported by the National Natural Science Foundation of China(10571176)by funds from Chinese Academy of Sciences
文摘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 witha 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.
基金Supposed by the National High-Technology Research and Development Programme of China under Grant No 2006AA01Z419, the Major Research Plan of the National Natural Science Foundation of China under Grants No 90604023, the National Research Foundation for the Doctoral Programme of Higher Education of China under Grant No 20040013007, the Foundation of National Laboratory for Modern Communications under Grant No 9140C1101010601, and the Natural Science Foundation of Beijing under Grant No 4072020.
文摘We propose a new multiparty simultaneous quantum direct communication scheme based on Creen-Horne- Zeilinger （CHZ） states and dense coding. For achieving high efficiency without leaking any information, four encoding schemes are prepared in advance. The present scheme has the capacity of transmitting （M ＋ 1）M classical bits per group of M-particle CHZ states when there exist M parties. The technique of rearranging particles makes the legal users coequally exchange their messages in the same length. Both high efficiency and excellent security against the common attacks are virtues of this new scheme.
