The quantum internet holds promise for performing quantum communication, such as quantum teleportation and quantum key distribution (QKD), freely between any parties all over the globe. Such a future quantum network, depending on the communication distance of the requesting parties, necessitates to invoke several classes of optical quantum communication such as point-to-point communication protocols, intercity QKD protocols and quantum repeater protocols. Recently, Takeoka, Guha and Wilde (TGW) have presented a fundamental rate-loss tradeoff on quantum communication capacity and secret key agreement capacity of any lossy channel assisted by unlimited forward and backward classical communication [Nat. Commun. 5, 5235 (2014)]. However, this bound is applicable only to the simplest class of quantum communication, i.e., the point-to-point communication protocols, and it has thus remained open to grasp the potential of a `worldwide' quantum network. Here we generalize the TGW bound to be applicable to any type of two-party quantum communication over the quantum internet, including other indispensable but much more intricate classes of quantum communication, intercity QKD protocols and quantum repeater protocols. We also show that there is essentially no scaling gap between our bound and the quantum communication efficiencies of known protocols. Therefore, our result, corresponding to a fundamental and practical limitation for the quantum internet, will contribute to design an efficient quantum internet in the future.
