Table 1 Control sequence and inseparability parameters for various entangled states.

T(t) and θ(t) are controlled by the sequence in Fig. 2B with the setting values (T1, T2, … ) and (θ1, θ2, … ) defined in this table. φ(t) is also controlled to measure the inseparability parameter for each state. The generated state is inseparable when each inseparability parameter is below 1 (ℏ = 1/2). The expression of inseparability parameters is given in (11, 14, 20, 21).

Type of entanglement(T1, T2, … )1, θ2, … )Inseparability parameterMeasured value
EPR state(1,12,1)(90°, 0°)[Δ(x̂1x̂2)]2+[Δ(p̂1+p̂2)]20.44 ± 0.01
3-mode GHZ state(1,13,12,1)(90°, 180°, 0°)[Δ(x̂1x̂2)]2+[Δ(p̂1+p̂2+p̂3)]20.65 ± 0.01
[Δ(x̂2x̂3)]2+[Δ(p̂1+p̂2+p̂3)]20.67 ± 0.01
[Δ(x̂1x̂3)]2+[Δ(p̂1+p̂2+p̂3)]20.70 ± 0.01
2-mode cluster state(1,12,1)(90°, 90°)[Δ(p̂1x̂2)]2+[Δ(p̂2x̂1)]20.42 ± 0.01
3-mode cluster state (graph 1)(1,23,12,1)(90°, 90°, 90°)[Δ(p̂1x̂2)]2+[Δ(p̂2x̂1x̂3)]20.56 ± 0.01
[Δ(p̂3x̂2)]2+[Δ(p̂2x̂1x̂3)]20.54 ± 0.01
[Δ(p̂1p̂3)]2+[Δ(p̂2x̂1x̂3)]20.60 ± 0.01
3-mode cluster state (graph 2)(1,13,12,1)(90°, 180°, 90°)[Δ(p̂1x̂3)]2+[Δ(p̂3x̂1x̂2)]20.69 ± 0.01
[Δ(p̂2x̂3)]2+[Δ(p̂3x̂1x̂2)]20.65 ± 0.01
[Δ(p̂1p̂2)]2+[Δ(p̂3x̂1x̂2)]20.63 ± 0.01