As the simultaneous eigenstates of a complete set of commuting observables (CSCO) consisting of threebody operators of the form σ1ασ2βσrsγ, the construction of entangled states for a three-particle system is inv...As the simultaneous eigenstates of a complete set of commuting observables (CSCO) consisting of threebody operators of the form σ1ασ2βσrsγ, the construction of entangled states for a three-particle system is investigated. It is shown that there exist 54 different sets of operators (each containing four commuting three-body operators with their product being -1) and any three members of each set constitute a CSCO. It is found that 54 different sets of maximally entangled states can be constructed, including the usual GHZ (Greenberg-Horne-Zeilinger) state as a special case. Once a preferential representation is adopted, all of them can be expressed as a GHZ-like form. Moreover, there also exist 18sets of partially entangled states, where only two particles are entangled.展开更多
W. Dur et al. have shown that it is impossible to obtain a GHZ state from one copy of arbitrary W-class state via local operations and classical communication （LOCC） [W. Dur, G. Vidal, and J.I. Cirac, Phys. Rev. A ...W. Dur et al. have shown that it is impossible to obtain a GHZ state from one copy of arbitrary W-class state via local operations and classical communication （LOCC） [W. Dur, G. Vidal, and J.I. Cirac, Phys. Rev. A 62 （2000） 062314]. In our paper, the more general case is carefully investigated. We first show that, with a supply of two copies of arbitrary W-class state, we can always construct an explicit procedure to distill a GHZ state with a nonzero probability. Then based on this result, a simple procedure for distilling GHZ state from n copies of arbitrary W-class state is presented. Finally, we briefly discuss the applications.展开更多
文摘As the simultaneous eigenstates of a complete set of commuting observables (CSCO) consisting of threebody operators of the form σ1ασ2βσrsγ, the construction of entangled states for a three-particle system is investigated. It is shown that there exist 54 different sets of operators (each containing four commuting three-body operators with their product being -1) and any three members of each set constitute a CSCO. It is found that 54 different sets of maximally entangled states can be constructed, including the usual GHZ (Greenberg-Horne-Zeilinger) state as a special case. Once a preferential representation is adopted, all of them can be expressed as a GHZ-like form. Moreover, there also exist 18sets of partially entangled states, where only two particles are entangled.
基金National Natural Science Foundation of China under Grant No.10404039
文摘W. Dur et al. have shown that it is impossible to obtain a GHZ state from one copy of arbitrary W-class state via local operations and classical communication （LOCC） [W. Dur, G. Vidal, and J.I. Cirac, Phys. Rev. A 62 （2000） 062314]. In our paper, the more general case is carefully investigated. We first show that, with a supply of two copies of arbitrary W-class state, we can always construct an explicit procedure to distill a GHZ state with a nonzero probability. Then based on this result, a simple procedure for distilling GHZ state from n copies of arbitrary W-class state is presented. Finally, we briefly discuss the applications.
