Fig. 1. Visualization of QC protocol. A quantum server distributes the entangled state to all legitimate participants. They establish a common key based on multipartite quantum correlations. The N participants are notified through the QC protocol, where N participants are named as Bobj (j=1,2,…,N).

Fig. 2. Schematic of the experimental setup. NOPA1,2, nondegenerate optical parametric amplifier; PM, phase modulator; AM, amplitude modulator; HWP1,2, half-wave plate; PBS1,2, polarizing optical beam splitter; DBS, dichroic beam splitter; BS1, 90/10 optical beam splitter; BS2, 50/50 optical beam splitter; BS3, 80/20 (90/10) optical beam splitter; HR, mirror with high reflection; BHD1−4, balanced homodyne detector. (a^1,a^4) and (a^2,a^3) are phase-quadrature and amplitude-quadrature squeezed states, respectively. b^1,b^2,b^3, and b^4 combine a quadripartite GHZ state.

Fig. 3. Calculated key rate k of the CV QC system versus the transmission loss when the thermal noise variances are taken as ω=1.5 (red line), ω=3.5 (cyan line), and ω=5.5 (blue line), respectively.

Fig. 4. Calculated dependences of the key rate k on the transmission loss for different squeezing factors r and the extra noise factor r′. The red, green, and blue traces correspond to squeezing factors r of 0.46, 0.92, and 1.38 when r′ equals r, respectively.

Fig. 5. Measured variances of the amplitude and phase quadratures and the cross correlation variances of the Bobs’ received modes b^j′ when (a)–(f) 1−η=0.1 and (g)–(l) 1−η=0.2, respectively. (a), (g) Δ2x^B1; (b), (h) Δ2x^B2; (c), (i) Δ2p^B1; (d), (j) Δ2p^B2; (e), (k) Δ2(x^B1+x^B2); (f), (l) Δ2(p^B1+p^B2). The black and red lines correspond to the SNL and corresponding noise power, respectively. The analysis frequency is 3 MHz and the measurement parameters of the SA: RBW 30 kHz; VBW 30 Hz.

Fig. 6. Calculated key rate k and experiment result versus transmission loss. Two different transmission losses of the lossy channels are investigated, 1−η=0.1 and 1−η=0.2. Using the experimentally determined parameters r=0.46 and r′=0.58, the red trace curves the theoretical result of the QC key rate versus transmission loss, while the data points are numerically calculated key rate k from experimentally obtained CM VB.