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A symmetric device-independent quantum key distribution (DIQKD) protocol isproposed in this paper, with Holevo limit and subadditivity of von Neumannentropy, one can bound Eve's ability with collective attack. Together withsymmetry of this protocol, the state Eve prepared for Alice and Bob, and at thesame time, her eavesdropping on Alice's and Bob's measurements can bedefinitely inferred at the assumption that Eve aims at maximizing herinformation gain. The optimal state under this circumstance can be solelybounded with Alice and Bob's statistical results on the quantity ofClauser-Horne-Shimony-Holt (CHSH) polynomial $S$, that is, our symmetric DIQKDhas the same secure basis as that of Ekert91 protocol.

Symmetric Device-Independent Quantum Key Distribution Against General Attack