Privacy of a lossy bosonic memory channel

Quantum communications concern the study of quantum channels that also use continuous alphabets [1]. These can be modeled by bosonic field modes whose phase space quadratures enable for continuous variable encoding/decoding. Lossy bosonic channel, which consists of a collection of bosonic modes that lose energy en route from the transmitter to the receiver, belongs to the class of Gaussian channels which provide a fertile testing ground for the general theory of quantum channels’ capacities [2] and are easy to implement experimentally with high accuracy level (beam splitters or squeezers are examples of Gaussian operations) [1]. Hence, the increasing attention devoted to channels with memory effects, where the noise may be strongly correlated between uses of the channel, has been extended to bosonic channels [3]. The main motivation that has led to investigate memory effects in such channels has been the possibility to enhance their classical capacity by means of entangled inputs [4, 5]. Thus, the quest for effectiveness of entanglement inputs in other kind of capacities. Here we study the private classical information capacity [6] of a lossy bosonic memory channel. We use the model introduced in Ref.[4] where the memory effects are realized by considering quantum correlations among environments acting on different channel uses [3]. We then analyze the security (privacy) of the channel when there is a third dishonest party, who captures the information lost during the process of transmission between the sender and the receiver, i.e. the eavesdropper accesses the environment’s final state. We shall show that entangled inputs can enhance the private classical information capacity [6], but not above that of unentangled inputs in absence of memory. This is in contrast with what happen for simple classical information capacity [4, 5].