Fundamental limits of quantumsecure covert communication over bosonic channels. We investigate the fundamental limit of quantumsecure covert communication over the lossy thermal noise bosonic channel, the quantummechanical model underlying many practical channels. We assume that the adversary has unlimited quantum information processing capabilities as well as access to all transmitted photons that do not reach the legitimate receiver. Given existence of noise that is uncontrolled by the adversary, the square root law (SRL) governs covert communication: up to c*sqrtn covert bits can be transmitted reliably in n channel uses. Attempting to surpass this limit results in detection with unity probability as n approaches infinity. Here we present the expression for c, characterizing the SRL for the bosonic channel. We also prove that discretevalued coherent state quadrature phase shift keying (QPSK) constellation achieves the optimal c, which is the same as that achieved by a circularlysymmetric complexvalued Gaussian prior on coherent state amplitude. Finally, while binary phase shift keying (BPSK) achieves the Holevo capacity for noncovert bosonic channels in the low received signaltonoise ratio regime, we show that it is strictly suboptimal for covert communication.

Practical covert quantum key distribution with decoystate method Covert communication methods are used in the communication with high security level. When it turns to quantum communication, covertness is also an important concern which is firstly discussed by Arrazola and Scarani (Phys Rev Lett, 117:250503, 2016). To make quantum key distribution (QKD) protocol more suitable in the scenarios need high security, we propose a covert QKD protocol with decoystate method in this paper. The secure key rate and covertness of the covert decoystate QKD are proved. We compare the performance of the covert decoystate QKD with those of the original decoystate QKD and covert QKD without decoy states in numerical simulations. It shows that (1) the covert decoystate QKD can have a performance comparable to the original decoystate QKD protocol besides its covertness; (2) the covert decoystate QKD can have a considerable improvement of transmission distance over covert QKD without decoy states at the cost of a small change of covertness parameter. Furthermore, the statistical fluctuation due to the finite length of data is also taken into account based on the Gaussian analysis method.