Continuous-variable quantum secure direct communication against dual-sequence Gaussian attacks with quantum memory

Quantum secure direct communication (QSDC) promotes high security and instantaneousness in communication by conveying secret messages directly via the quantum channel.In particular, the continuous variable (CV) scheme of QSDC is already compatible with current room-temperature telecommunication networks and is very robust to the free-space background noise, making it a unique choice in certain applications.However, to date, the security proofs of CV-QSDC are poorly advanced, as the eavesdropper Eve in these proofs is limited, either can not apply the optimal collective measurements, or does not have full access to the quantum channel.In this paper, we refine and advance the previous theory in this area, providing a tight secrecy capacity bound for the CV-QSDC protocol.We study the secrecy capacity achievable by the two-step scheme, for both (one-mode) collective Gaussian attack and two-mode Gaussian attack, from the standard Markovian assumption on the environment to a more challenging scenario with a time-like and spatial non-Markovian model.Numerical results show that the best attack strategy for Eve is the entangled attack using maximally entangled states (with a positive correlation parameter).More interestingly, we find that the protocol with the standard Markovian model can, in theory, achieve a longer transmission distance in the communication channel affected by high thermal noise.