Extended analysis of the Trojan-horse attack in quantum key distribution

The discrete-variable quantum key distribution protocols based on the 1984 protocol of Bennett and Brassard (BB84) are known to be secure against an eavesdropper, Eve, intercepting the flying qubits and performing any quantum operation on them. However, these protocols may still be vulnerable to side-channel attacks. We investigate the Trojan-horse side-channel attack where Eve sends her own state into Alice's apparatus and measures the reflected state to estimate the key. We prove that the separable coherent state is optimal for Eve among the class of multimode Gaussian attack states, even in the presence of thermal noise. We then provide a bound on the secret key rate in the case where Eve may use any separable state.