Experimental measurement-device-independent quantum digital signatures over a metropolitan network

Quantum digital signatures (QDSs) provide a means for signing electronic communications with information-theoretic security. However, all previous demonstrations of quantum digital signatures assume trusted measurement devices. This renders them vulnerable against detector side-channel attacks, just like quantum key distribution. Here we exploit a measurement-device-independent (MDI) quantum network, over a metropolitan area, to perform a field test of a three-party MDI QDS scheme that is secure against any detector side-channel attack. In so doing, we are able to successfully sign a binary message with a security level of about ${10}^{-7}$. Remarkably, our work demonstrates the feasibility of MDI QDSs for practical applications.

Figure 1

Measurement-device-independent QDS experiment in a Hefei optical fiber network. (a) Birds-eye view of the MDI QDS experiment. Alice $A$ is located in the Animation Industry Park ($\mathrm{N}{31}^{\circ }{50}^{\prime }6.{24}^{\prime \prime }, \mathrm{E}{117}^{\circ }{7}^{\prime }52.{08}^{\prime \prime }$), Bob $B$ at the administrative committee of Hefei ($\mathrm{N}{31}^{\circ }{47}^{\prime }4.{56}^{\prime \prime }, \mathrm{E}{117}^{\circ }{12}^{\prime }58.{04}^{\prime \prime }$), Charlie $C$ in an office building ($\mathrm{N}{31}^{\circ }{50}^{\prime }56.{84}^{\prime \prime }, \mathrm{E}{117}^{\circ }{16}^{\prime }50.{14}^{\prime \prime }$), and Eve $E$ at the University of Science and Technology of China ($\mathrm{N}{31}^{\circ }{50}^{\prime }7.{56}^{\prime \prime }, \mathrm{E}{117}^{\circ }{12}^{\prime }58.{04}^{\prime \prime }$). The $A-E-B$ ($A-E-C$) quantum link is used to perform the MDI KGP, which generates correlated $L$-bit strings $A_m^B$ and $K_m^B$ ($A_m^C$ and $K_m^C$) between Alice and Bob (Charlie). The $B-E-C$ quantum link is used to carry out the MDI QKD scheme, which generates a secure key between Bob and Charlie. This key is used to one-time pad encrypt the information exchanged by these two users during the symmetrization step of the MDI QDS scheme. (b) Alice's setup. The setups of Bob and Charlie are identical to the one of Alice. The internally modulated laser generates phase-randomized coherent-state signal pulses. The first intensity modulator (IM) removes the overshoot rising edge of the signal pulses. The following two IMs implement the decoy state method [21, 22, 23]. An asymmetrical Mach-Zehnder interferometer (AMZI) with a phase shifter (PS), in combination with two IMs and one phase modulator (PM), form a qubit encoder, which realizes a time-bin phase encoding. The attenuator (Att) is electrically controlled; it can quickly and automatically change the intensity of the outgoing signals to realize either the Hong-Ou-Mandel interference or single-photon level preparation. Spurious emission is removed by means of a dense wavelength division multiplexor (DWDM). (c) Eve's setup. An $8\times 4$ mechanical optical switch (MOS) implements the routing function. An electric polarization controller (EPC), a polarization beam splitter (PBS), and a superconducting nanowire single-photon detector (SNSPD) form the polarization feedback system. The beam splitter (BS) and two SNSPDs are used to implement the Bell state measurement.

Figure 2

Schematic diagram of the MDI QDS setup. The channels between the Alice-Eve, Bob-Eve, and Charlie-Eve links are quantum channels (QC); they are denoted by dashed lines. The Alice-Bob, Alice-Charlie, and Bob-Charlie links are also connected through authenticated classical channels (CC); these channels are represented with solid lines. The MDI QDS protocol requires that Bob and Charlie previously share a secret key. For this, they implement a MDI QKD protocol in which Eve acts as a relay. Each of Alice, Bob, and Charlie has one laser source that generates phase-randomized weak coherent pulses that encode different Bennett-Brassard states by means of a state encoding setup. Also, they generate decoy states with an intensity modulator. This modulator is denoted by Decoy IM in the figure. Eve is supposed to perform a Bell state measurement on the incoming signals.