BBM92 Quantum Key Distribution with Non-Maximally Entangled States in Random Scattering Media Using Kraus Operators

Scattering environments place severe constraints on the security of quantum communication systems, as they induce decoherence mechanisms that degrade entanglement. To quantify these effects, we analyze the performance of the BBM92 protocol in terms of the quantum bit error rate (QBER) and the secret key rate (SKR), considering non-maximally entangled photon pairs transmitted through a quantum channel affected by amplitudedamping and depolarizing effects, described by Kraus operators. We derive closed-form analytical expressions for the QBER and SKR, which establish theoretical security bounds for secure key generation under non-ideal conditions.