As the simultaneous eigenstates of a complete set of commuting observables (CSCO) consisting of three-body operators of the form , 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 18 sets of partially entangled states, where only two particles are entangled.As the simultaneous eigenstates of a complete set of commuting observables (CSCO) consisting of three-body operators of the form , 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 18 sets of partially entangled states, where only two particles are entangled.

Communications in Theoretical PhysicsJul 15, 20040 citations

Multi-particle entanglement

Dirk Bouwmeester, Jian-Wei Pan, Matthew Daniell +2 more

Springer eBooksJun 1, 20012 citations

The quantum entanglement of three particle systems

光太郎上原

Jul 1, 20070 citations

Construction of GHZ-Like States for a Three-Particle （Spin 1／2） System

RUANMan-Qi, Xugang, ZENGJin-Yan

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.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.

理论物理通讯：英文版Jan 1, 20040 citations

Scaling of genuine multiparticle entanglement close to a quantum phase transition

Martin Hofmann, Andreas Osterloh, Otfried Gühne

We investigate the scaling and spatial distribution of genuine multiparticle entanglement in three- and four-spin reduced states of the one-dimensional $XY$ model at the quantum phase transition. We observe a logarithmic divergence, show that genuine three- and four-particle entanglement obeys finite-size scaling of the $XY$ model and demonstrate that the genuine three-particle entanglement has a finite spatial range.We investigate the scaling and spatial distribution of genuine multiparticle entanglement in three- and four-spin reduced states of the one-dimensional $XY$ model at the quantum phase transition. We observe a logarithmic divergence, show that genuine three- and four-particle entanglement obeys finite-size scaling of the $XY$ model and demonstrate that the genuine three-particle entanglement has a finite spatial range.

arXiv:1309.2217Physical Review BApr 2, 201488 citations

Generating three-particle entanglement states

Xiao-Feng Fan, Tao Yang, Jian Li +2 more

Physics Letters AJun 1, 20012 citations

We investigate the scaling and spatial distribution of genuine multiparticle entanglement in three- and four-spin reduced states of the one-dimensional

XY

model at the quantum phase transition. We observe a logarithmic divergence, show that genuine three- and four-particle entanglement obeys finite-size scaling of the

XY

model and demonstrate that the genuine three-particle entanglement has a finite spatial range.