Fig. 1. Schematic diagram of the quantum e-commerce. TTP-TP acts as a bridge among the merchant, the client, the LC, and the bank, with pre-distributed keys among all parties. It is necessary to pre-distribute keys among the bank and the client in order to safeguard the security of the payment. Firstly, the merchant and the client sign a subscription protocol. Next, the client and TTP-TP execute the payment protocol I. The merchant and the LC sign a transport protocol, and the goods are delivered to the clients. Finally, the LC and the client sign a reception protocol, and the TTP-TP takes a commission and executes payment protocol II.

Fig. 2. Schematic diagrams of the subscription and payment protocols. (a) Subscription protocol. Firstly, the merchant drafts and signs the contract, and then sends the signature and the contract to the client. The client approves the contract and sends the merchant’s signature and contract to the TTP-TP. The TTP-TP publishes the key KZS=KXS⊕KYS. The client then verifies the signature. Once the validation of the signature is confirmed, the TTP-TP then performs another validation to ensure the legitimacy of the signature and the integrity of the contract. If the TTP-TP’s signature validation passes, the sign of the subscription protocol is complete. (b) Payment protocol I. The client creates an account at the bank and receives an identifier (ID) CID. The bank generates a cardholder token C based on each client’s ID. By using the d-bit secure key KYCP, the bank encrypts the cardholder token C and sends it to the client. The bank generates a one-time payment token P and encrypts it using the h-bit secure key KYPP, and then sends the encrypted token to the client. The client then signs the file WP consisting of the cardholder token C, the payment token P, the TTP-TP’s ID TID, and the payment amount M, and sends {CID,SCP} to the TTP-TP. The TTP-TP combines the received information with their own private TID and the payment amount M, and forwards them to the bank. The bank verifies the signature and completes the payment.

Fig. 3. Experimental quantum e-commerce. (a) Time allocation of the optical switches. We evenly divide the working time of the optical switches into seven intervals. The subscription protocol, the transport protocol, and the reception protocol are allocated two intervals each, while the payment protocol II occupies one interval. During the time slot when the TTP-TP is conducting key distribution with the client, the bank and the client will suspend their key distribution operations. Outside of this time slot, the bank and the client will recover their key distribution. (b) Experimental setup. The TTP-TP prepares quantum states and sends them to the merchant, the client, the LC, and the bank, respectively. Moreover, the bank sends the prepared quantum states to the client. After receiving the quantum signals, they measure both quadratures of the quantum states using heterodyne detection. By data post-processing, keys are shared between the parties. Then the quantum e-commerce is implemented following the procedures in Section 2. IQ, in-phase and quadrature modulator; BS, beam splitter; PD, photoelectric detector; HD, heterodyne detector; VOA, variable optical attenuator; OS, optical switch; PC, polarization controller.

Fig. 4. Digital signal processing in the quantum e-commerce. (a) Generation of the quantum signal and the pilot tone at the transmitter. The TTP-TP and the bank generate modulation signals with quantum true random numbers, which are boosted to a sampling rate of 12.5 Gsamples/s by upsampling. Then, the upsampling signals are pulse shaped and frequency up-shifted to 1.2 GHz. Finally, the pilot tone (400 MHz sinusoidal signal) is added in. (b) Extraction of the quantum signal at the receiver. The fast Fourier transform (FFT) transforms the acquired signal into frequency domain to retrieve the frequency of the pilot tone. The quantum signal and the pilot tone are downconverted to the baseband and low-pass filtered to eliminate the out-of-band noises. The phase of the quantum signal is recovered using that of the pilot tone.

Fig. 5. Excess noise of the CV-QKD between different participants at 80 km single-mode fiber. The solid circles denote experimental points; the dashed line indicates the average value of the excess noise.

Fig. 6. Contract signing rates, payment rates, and transaction rates versus the distance in quantum e-commerce. (a) Signing rates for the subscription protocol, the transport protocol, and the reception protocol. (b) Payment rates for the payment protocol I and payment protocol II. (c) Transaction rates for the complete quantum e-commerce. The solid line denotes the result of the theoretical simulation. Circles, triangles, and pentagrams denote the experimental results.

Fig. 7. Transaction rate versus the signature file size in quantum e-commerce. The blue line indicates the transaction rates of a complete quantum e-commerce with 10−9 security level at 80 km single-mode fiber. The shadow area denotes a higher security level of ξtot<10−9. For a file of 100 megabits size, we can still achieve a secure transaction rate of 341 per second.