Quantum Key Recycling with Optimal Key Recycling Rate based on Error Rate

Abstract: We propose a new Quantum Key Recycling (QKR) protocol, which can tolerate the noise in the quantum channel. Our QKR protocol recycles the used keys according to the error rate. The key recycling rate of the pre-shared keys in our QKR protocol is optimized depending on the real error rate in the quantum channel. And our QKR protocol has higher efficiency than the exiting QKR protocol with error-tolerance. The security proof shows the security of the recycled keys is universal composable.