Fig. 1. Schematic diagram of free-space QSDC system. Att, attenuator; BS, beam splitter; DL, delay line; FPGA, field-programmable gate array; FR, Faraday rotator; PBS, polarization beam splitter; PC, polarization controller; PM, phase modulator; PMCIR, polarization-maintaining circulator; PMFC, polarization-maintaining fiber coupler; SPD, single-photon detector; TFOC, triplet fiber-optic collimator. Blue, yellow, and red lines are the electric line, optical fiber line, and free-space path, respectively.

Fig. 2. Interference fringes. Driving voltage ranges from −6  V to +6  V with a half-wave voltage 4.8 V and a step of about 0.1 V. The interference fringe of a single-trip (photons transmitted from Bob-to-Alice) is obtained from Alice’s detection. More specifically, the counts are recorded by Alice’s SPD at each step when she drives the voltage of her PM. By contrast, when the photons are received by Bob (after their trip Bob-Alice-Bob), he drives the voltage of his PM and records counts by his SPD to obtain the interference fringe of the round-trip.

Fig. 3. Error rates during image file transmission. Dashed lines represent the mean values of DBER, and dash-dotted lines show the mean values of QBER. The definition of DBER and QBER is given in Section 2.A, while the experimental approach for accessing them is introduced in Section 2.B.

Fig. 4. Illustration of Eve’s attack strategies. n, the number of photons in a pulse in the forward quantum channel; EμBA is the error rate of the Bob-Alice channel, which is also called as DBER; QμBA, the overall signal gain of Alice; edetBA, the erroneous signal detection of Alice; ρBE, the joint state after Eve’s attack in the forward quantum channel; QμBAE, the overall signal gain of Eve; ρBAE, the joint state after Alice’s information encoding and Eve’s attacks in the two quantum channels; EμBAB is QBER; QμBAB, the overall signal gain of Bob; edetBAB is the erroneous signal detection of Bob.

Fig. 5. Secrecy capacities versus the attenuation given the collective attack as well as the PNS and USD attack under the framework of GLLP analysis. The curves labeled by different markers represent the data with different mean photon numbers.

Fig. 6. Comparison of the secrecy capacities calculated by the GLLP theory and the decoy-state method. Simulations in the decoy-state method using μ=0.1, ν1=0.07, ν2=0.0445, and ν3=0.03 and in the GLLP theory using μ=0.1 are performed. In the secrecy capacity Cs,1+2, we have considered the contribution both from single-photon states and two-photon states, while Cs,1 has not considered the contribution from two-photon states. The two yellow areas represent the contribution of two-photon states to the secrecy capacity.