One-sided measurement-device-independent quantum key distribution

Measurement-device-independent quantum key distribution (MDI-QKD) protocol was proposed to remove all the detector side channel attacks, while its security relies on the trusted encoding systems. Here we propose a one-sided MDI-QKD (1SMDI-QKD) protocol, which enjoys detection loophole-free advantage, and at the same time weakens the state preparation assumption in MDI-QKD. The 1SMDI-QKD can be regarded as a modified MDI-QKD, in which Bob's encoding system is trusted, while Alice's is uncharacterized. For the practical implementation, we also provide a scheme by utilizing coherent light source with an analytical two decoy state estimation method. Simulation with realistic experimental parameters shows that the protocol has a promising performance, and thus can be applied to practical QKD applications.

Figure 1

Schematic diagram of 1SMDI-QKD. BSM denotes Bell state measurement; $A_i$ and $B_i$ ($i\in \{1,2\}$) denote the encoding basis of Alice and Bob. Alice and Bob prepare some quantum states and send them to an untrusted relay, Charlie, who is supposed to perform BSM and broadcast the results. Bob's encoding system is trusted, while Alice's is uncharacterized and assumed to output the quantum state in two-dimensional Hilbert space. The white box denotes the trusted device, the black box denotes the untrusted device, and the gray box denotes the uncharacterized device.

Figure 2

EPR denotes Einstein-Podolsky-Rosen state; BSM denotes the Bell state measurement. (a) Single-photon 1SMDI-QKD in which Alice's encoding system is uncharacterized. (b) Virtual-photon single-photon 1SMDI-QKD using the EPR source. Instead of preparing a BB84 state, Alice and Bob prepares an perfect EPR pair and sends one particle to an untrusted relay, Charlie, who performs BSM and broadcasts the measurement results. Alice and Bob measure their particles using the $A_1/A_2$ and $B_1/B_2$ bases, respectively. Alice's EPR source is perfect while the local detector is untrusted. This is equivalent to saying that Alice's encoding system is uncharacterized, implying the qubit state from Alice's encoding system [see Fig. 2] is basis independent. (c) Time-reversed single-photon 1SMDI-QKD. Since their measurement operations are commutable, the order of the measurements can be reversed. That is, Alice and Bob can perform the projective measurement after the BSM is performed. (d) Equivalent EPR-based 1SDI-QKD protocol. This is exactly the 1SDI-QKD in which an EPR source outputs qubits to Alice and Bob, and its security has been proven in Sec. 2. The black, white, and gray boxes denote the untrusted, trusted, and uncharacterized parts, respectively.

Figure 3

Basic setup of a decoy-state 1SMDI-QKD protocol. WCP denotes the weak coherent pulse, PM denotes the polarization modulator, IM denotes the intensity modulator, BS denotes the beam splitter, PBS denotes the polarization beam splitter, and D1, D2, D3, and D4 denote single-photon detectors. Alice and Bob prepare WCPs in a different BB84 polarization state randomly, then send them to Charlie to perform the Bell state measurement. A click in D1 and D4, or in D2 and D3, indicates a projection into the Bell state $|{\psi }^{-}\rangle =(|HV\rangle -|VH\rangle )/\sqrt{2}$, and a click in D1 and D2, or in D3 and D4 indicates a projection into the Bell state $|{\psi }^{+}\rangle =(|HV\rangle +|VH\rangle )/\sqrt{2}$. The black, white, and dashed boxes denote the untrusted, trusted, and uncharacterized parts, respectively.

Figure 4

Lower bound on the secret key rate $R$ versus communication distance between Alice and Bob. The experimental parameters used are listed in Table 2. The solid line denotes the asymptotic case, and the dashed line denotes the two decoy states case. The different color corresponds to different ${\eta }_s$. In particular, the red line denotes ${\eta }_s=1$, i.e., the MDI-QKD protocol. The intensities of the signal state used by Alice and Bob are optimized for the asymptotic case, and are $0.45,0.3,0.1,0.05$, for ${\eta }_s=1,0.95,0.9,0.85$, respectively. The intensity of the decoy states are fixed at 0.01 and 0.