In this commentary, we discuss the Device-Independent Conference Key Agreement (DICKA) protocol [Phys. A 97, 022307 (2018)]. We show that the proposed honest implementation fails because the perfectly correlated measurement results and the required violation of Bell`s inequality cannot be achieved at the same time, contrary to what is claimed. We also show through semi-indefinite programming that there can be no proper honest implementation in the tripartite environment, which makes the DICKA protocol incomplete. We present a security analysis of the Key Conference Agreement (CKA) in the most adversarial model of device independence (DI). Our protocol can be implemented by any experimental configuration capable of performing Bell tests [in particular the Mermin-Ardehali-Belinskii-Klyshko (MABK)] inequality), and security can in principle be achieved for any violation of the MABK inequality that detects a true multi-part entanglement between the N parties involved in the protocol. As a main tool, we deduce a direct physical link between mabk N-partite inequality and Clauser-Horne-Shimony-Holt (CHSH) inequality, which shows that some violations of MABK inequality correspond to a violation of CHSH inequality between one of the parties and the other N−1. We compare the asymptotic key rate for device-independent conferencing key agreement (DICKA) in case N−1 parties use device-independent quantum key distribution protocols to generate a shared key. We show that the DICKA protocol leads to better rates for certain noise regimes.
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If Ti=0 then C̃i=⊥, otherwise C̃i=wMABK(Ai′,B(1…N−1),i′,Xi,Y(1…N−1),i). Asymptotic key rate for N-DICKA (dotted lines) and for distributing a secret key between N parties via N−1 DIQKD protocols (solid lines) when each qubit has independent bit errors measured with a binary error rate (QBER) Q. From top to bottom, the lines correspond to N={3,4,5,6,7}. We observe that it is advantageous for the low-noise regime to use DICKA instead of (N−1)×DIQKD [11]. In general, the comparison between the two methods depends on the cost and noisy nature of generating GHZ states on paired EPR pairs. Sign up to receive regular email notifications from Physical Review A. We appreciate your continued efforts and commitment to advancing science and enabling us to publish the best physics journals in the world. And we hope you and your loved ones stay safe and healthy.
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