Deterministic Minimum-Leakage Continuous-Variable Quantum Key Distribution with Phase-Conjugated Twin Beams

Abstract

Minimum-leakage continuous-variable quantum key distribution suppresses Eve's Holevo information by engineering the signal ensemble at the state-preparation stage. Existing symmetric minimum-leakage protocols achieve this goal by heralding: Alice interferes two squeezed ensembles, measures one output mode, and sends the other to Bob. Here we propose a deterministic two-mode protocol that removes the Alice-side heralding step. Alice combines two oppositely squeezed Gaussian ensembles on a balanced beam splitter and transmits both output modes, which form phase-conjugated twin beams. We show that this protocol is related to the heralding protocol through a common entanglement-based source but corresponds to a different prepare-and-measure decomposition. In the very-large-squeezing limit, the two protocols give the same secret key rate per transmitted optical mode. For finite squeezing, however, the phase-conjugated twin-beam protocol requires approximately 3 dB less squeezing to achieve the same key rate. We further analyze correlated two-mode Gaussian attacks in which Eve injects ancillary modes with optimized inter-mode correlations. We find that the correlated attacks are slightly more efficient than independent attacks, but the advantage remains limited under the minimum-leakage condition. These results show that phase-conjugated twin beams provide a deterministic and experimentally appealing route to symmetric minimum-leakage CV-QKD.