Security Proof Against Collective Attacks for an Experimentally Feasible Semi-Quantum Key Distribution Protocol

Semi-quantum key distribution (SQKD) allows two parties (Alice and Bob) to create a shared secret key, even if one of those parties (say, Alice) is classical. However, most SQKD protocols suffer from practical security problems. The recently developed "Classical Alice with a Controllable Mirror" protocol [Boyer, Katz, Liss, and Mor, Phys. Rev. A 96, 062335 (2017)] is an experimentally feasible SQKD protocol, and it was proven robust, but not yet proved secure. Here we prove the security of the Mirror protocol against a wide class of quantum attacks (the "collective attacks") and evaluate the resulting key rate.