01494nas a2200133   4500000000100000008004100001260001500042100002100057700001900078700002100097245007100118856003700189520113400226       2026                            d  c09/03/20261 aLeonard Sikorski1 aŁukasz Pawela1 aPaweł Horodecki00aLimitations on quantum key repeaters for all key correlated states  uhttps://arxiv.org/abs/2206.009933 aQuantum key repeater is the backbone of the future Quantum Internet. It is an open problem to determine, for an arbitrary mixed bipartite state shared between the stations of a quantum key repeater, how much key can be generated between its two end-nodes. We place a novel bound on the quantum key repeater rate, which uses the relative entropy distance from, in general, entangled quantum states. It allows us to generalize bounds on key repeaters of M. Christandl and R. Ferrara [Phys. Rev. Lett. 119, 220506]. As in the latter article, we consider a scenario used for measurement-device-independent quantum cryptography. The derived bound, although not tighter, holds for a more general class of states, thereby avoiding the NP-hard separability problem. We show that the repeated key of the broad class of key correlated states can exceed twice the one-way distillable entanglement by at most the max-relative entropy of entanglement of its attacked version. We also provide a non-trivial upper bound on the amount of private randomness of a generic independent bit — a state containing one bit of ideal private randomness.