Measurement-device-independent quantum communication with an untrusted source

Measurement-device-independent quantum key distribution (MDI-QKD) can provide enhanced security compared to traditional QKD, and it constitutes an important framework for a quantum network with an untrusted network server. Still, a key assumption in MDI-QKD is that the sources are trusted. We propose here a MDI quantum network with a single untrusted source. We have derived a complete proof of the unconditional security of MDI-QKD with an untrusted source. Using simulations, we have considered various real-life imperfections in its implementation, and the simulation results show that MDI-QKD with an untrusted source provides a key generation rate that is close to the rate of initial MDI-QKD in the asymptotic setting. Our work proves the feasibility of the realization of a quantum network. The network users need only low-cost modulation devices, and they can share both an expensive detector and a complicated laser provided by an untrusted network server.

Figure 1

(a) A fiber-based quantum network with $N$ trusted lasers. (b) A quantum network with a single untrusted laser source.

Figure 2

Schematic diagram of a time-bin-encoding MDI-QKD with an untrusted laser source. The strong time-bin laser pulses are generated by a pulsed laser and an interferometer in the server (Charlie), and they are split into two groups by a beam splitter (BS). Once these pulses arrive at Alice (Bob), they pass through an optical filter (F), a monitoring unit with a BS and a classical intensity detector (ID), a phase modulator (PM1 and PM3) for phase randomization, and a variable optical attenuator (VOA). Then, the pulses are encoded by an encoder that consists of an intensity modulator (IM) and a PM, and they are reflected by a Faraday mirror (FM). Finally, the pulses from Alice and Bob interfere at Charlie's BS and are detected by two single-photon detectors (D0 and D1). The coincident counts are recorded by a time interval analyzer (TIA).

Figure 3

(a) The actual model for Fig. 2. All the internal loss of Alice or Bob is modeled as a $\lambda /(1-\lambda )$ beam splitter. (b) An equivalent virtual model. The loss is modeled as a ${\lambda }^{\prime }/(1-{\lambda }^{\prime })$ beam splitter. $q^{\prime }={\eta }_{\mathrm{ID}}(1-q)$, where ${\eta }_{\mathrm{ID}}\le 1$ is the efficiency of the imperfect intensity detector. ${\lambda }^{\prime }=q\lambda /q^{\prime }$. The virtual model, which has features from (a), is used to analyze the security of (a).

Figure 4

Simulation results. Red (light gray) curves are for an infinite number of signals. $M_{\mathrm{c}}$ denotes the mean of the photon number (per pulse) of Charlie's laser pulses. With $M_{\mathrm{c}}={10}^9$ and practical imperfections, MDI-QKD with an untrusted source can tolerate about a 195-km distance. At distances below 180 km, the key rates for the two cases (with trusted and untrusted sources) almost overlap. Blue (dark gray) curves are for a finite number of signals. A finite data size reduces the efficiencies for both cases. MDI-QKD with an untrusted source can still tolerate over 70 km of fiber with detectors with 20% efficiency.