Device-Independent Quantum Key Distribution with Local Bell Test

Device-independent quantum key distribution (DIQKD) in its current design requires a violation of a Bell’s inequality between two parties, Alice and Bob, who are connected by a quantum channel. However, in reality, quantum channels are lossy and current DIQKD protocols are thus vulnerable to attacks exploiting the detection loophole of the Bell test. Here, we propose a novel approach to DIQKD that overcomes this limitation. In particular, we propose a protocol where the Bell test is performed entirely on two casually independent devices situated in Alice’s laboratory. As a result, the detection loophole caused by the losses in the channel is avoided.

Popular Summary

Quantum key distribution (QKD) is a cryptographic primitive that allows two parties (Alice and Bob) to distribute secret keys using a (potentially insecure) quantum channel. Crucially, in contrast to public-key cryptography, QKD is information-theoretically secure; i.e., its security is obtained in the framework of information theory, and thus is secure even if the eavesdropper has unlimited computing power. The security of QKD, however, is often obtained under the assumption that Alice and Bob use very specific quantum states and measurements. In reality, this assumption is virtually impossible to meet, as almost all practical devices contain some inadvertent flaws.

Recently, “device-independent” QKD (DIQKD) has been proposed as a novel approach to tackle the problem of inadvertently flawed devices. The basic idea there is to base the security on the certification of nonlocal quantum correlations (shared between Alice and Bob); i.e., Alice and Bob perform a Bell test across the quantum channel to assess the quality of the quantum correlations. Even though the problem of inadvertently flawed devices is solved, DIQKD still has a crucial limitation in that it requires Alice and Bob to perform the Bell test with an almost lossless quantum channel. As a consequence, the maximum possible distance between Alice and Bob is drastically limited.

In our work, we present a novel type of DIQKD protocol that no longer suffers from this limitation. Specifically, our DIQKD protocol is based on the concept of the local Bell test; that is, Alice performs the Bell test entirely in her laboratory. Importantly, since the Bell test is no longer carried out across the quantum channel shared by Alice and Bob, the protocol can tolerate substantial losses in the quantum channel. Therefore, our protocol potentially allows key distribution over longer distances as compared to existing DIQKD protocols.

Figure 1

Topology: The protocol is inspired by the idea of the time-reversed BB84 protocol and involves an additional (untrusted) party, Charlie. Charlie is supposed to make an entangling measurement (ideally, a Bell-state measurement) on quantum states sent by Alice and Bob. He outputs either a pass or fail to indicate whether the measurement was successful. If successful, he additionally outputs two bits to be used by Alice to make correcting bit-flip operations.

Figure 2

Secret fraction $\ell /m_x$ as a function of the tolerated efficiency of Charlie’s operation ${\eta }_{\mathrm{tol}}$ (including channel losses): We consider a depolarizing channel with a fixed error rate $Q_{\mathrm{tol}}=1\%$ and $S_{\mathrm{tol}}=V2\sqrt{2}$. The solid curves [asymptotic rates, Eq. (2)] are obtained with $V=0.999$ and $V=0.99$ from left to right. The right dashed curve [finite-key analysis, Eq. (1)] is obtained by choosing $S_{\mathrm{tol}}=2\sqrt{2}$, ${\mathrm{leak}}_{\mathrm{EC}}=m_{x}1.1h(Q_{\mathrm{tol}}+\mu )$, ${\epsilon }_{\sec }={10}^{-8}$, and ${\epsilon }_{\mathrm{cor}}={10}^{-12}$, where the classical postprocessing block size $m_x$ is of the order of ${10}^8$ bits.