Author Affiliations
1State Key Laboratory of Precision Spectroscopy, East China Normal University, Shanghai 200062, China2Collaborative Innovation Center of Extreme Optics, Shanxi University, Taiyuan 030006, Chinashow less
Fig. 1. A simplified diagram of quadripartite entanglement and an energy level diagram of rubidium-85: (a) C
0 and C
2 are vacuum states, Pr
0 and Pr
2 are coherent states; C
1 and
are the twin beams generated by the first four-wave mixing process, C
3 and
are the twin beams generated by the second four-wave mixing process; Pr
1 and Pr
3 are produced by mixing beams
and
through a linear beam splitter; (b) the double Λ energy level structure of D1 line in rubidium-85,
Δ and
δ represent one-photon detuning and two-photon detuning respectively.
Fig. 2. The smallest symplectic eigenvalue v of all 1 × 3 scenarios, as a function of the power gains G1 and G2: (a) C1 is partially transposed; (b) Pr1 is partially transposed; (c) Pr3 is partially transposed; (d) C3 is partially transposed.
Fig. 3. The smallest symplectic eigenvalues v of all 2 × 2 scenarios, as a function of the power gains G1 and G2: (a) C1 and Pr1 arepartially transposed; (b) C1 and Pr3 are partially transposed; (c) C1 and C3 are partially transposed.
Fig. 4. Effect of the transmissivity of the linear beam splitter on the quadripartite entanglement of the system: (a) C1 is partially transposed; (b) Pr1 is partially transposed; (c) Pr3 is partially transposed; (d) C3 is partially transposed; (e) C1 and Pr1 are partially transposed; (f) C1 and Pr3 are partially transposed; (g) C1 and C3 are partially transposed.
Fig. 5. The smallest symplectic eigenvalues v of all tripartite states as a function of power gains G1 and G2: (a)−(c) The smallest symplectic eigenvaluesv of tripartite state composed of C1, Pr1 and Pr3; (d)−(f) the smallest symplectic eigenvaluesv of tripartite state composed of C1, Pr1 and C3; (g)−(i) the smallest symplectic eigenvaluesv of tripartite state composed of C1, Pr3 and C3; (j)−(l) the smallest symplectic eigenvaluesv of tripartite state composed of Pr1, Pr3 and C3.
Fig. 6. The smallest symplectic eigenvalues v of all bipartite states as a function of power gains G1 and G2: (a) The smallest symplectic eigenvalues v of bipartite state composed of C1 and Pr1; (b) the smallest symplectic eigenvalues v of bipartite state composed of C1 and Pr3; (c) the smallest symplectic eigenvalues v of bipartite state composed of C1 and C3; (d) the smallest symplectic eigenvalues v of bipartite state composed of Pr1 and Pr3; (e) the smallest symplectic eigenvalues v of bipartite state composed of Pr1 and C3; (f) the smallest symplectic eigenvalues v of bipartite state composed of Pr3 and C3.
数目 | 二分形式 | | 数目 | 二分形式 | 1 | 1|234 | | 2 | 2|134 | 3 | 3|124 | 4 | 4|123 | 5 | 12|34 | 6 | 13|24 | 7 | 14|23 | | |
|
Table 1. Seven partitions of quadripartite state.
四组份态的七种二分形式