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

We propose a new Quantum Key Recycling (QKR) protocol, which recycles used keys according to the error rate. Our QKR protocol can tolerate the noise in the quantum channel. The earlier studies also proposed QKR protocols with noise tolerance. Unfortunately, there is a common security loophole in these protocols. Our QKR protocol is designed to avoid this security loophole, and the key recycling rate of the pre-shared keys is optimized depending on the noise level. The security proof shows the security of the recycled keys is universal composable.