We derive a capacity formula for attenuation channels assisted by quantum linear amplifiers when the input signal states are restricted to Gaussian states with the same correlation matrix. A phase insensitive linear amplifier and a phase sensitive linear amplifier are compared by using this formula.
We consider a quantum bosonic channel that couples the input mode via a beam splitter or two-mode squeezer to an environmental mode that is prepared in an arbitrary state. We investigate the classical capacity of this channel, which we call a non-Gaussian attenuator or amplifier channel. If the environment state is thermal, we of course recover a Gaussian phase-covariant channel whose classical capacity is well known. Otherwise, we derive both a lower and an upper bound to the classical capacity of the channel, drawing inspiration from the classical treatment of the capacity of non-Gaussian additive-noise channels. We show that the lower bound to the capacity is always achievable and give examples where the non-Gaussianity of the channel can be exploited so that the communication rate beats the capacity of the Gaussian-equivalent channel (i.e. the channel where the environment state is replaced by a Gaussian state with the same covariance matrix). Finally, our upper bound leads us to formulate and investigate conjectures on the input state that minimizes the output entropy of non-Gaussian attenuator or amplifier channels. Solving these conjectures would be a main step toward accessing the capacity of a large class of non-Gaussian bosonic channels.
We consider a quantum bosonic channel that couples the input mode via a beam splitter or two-mode squeezer to an environmental mode that is prepared in an arbitrary state. We investigate the classical capacity of this channel, which we call a non-Gaussian attenuator or amplifier channel. If the environment state is thermal, we of course recover a Gaussian phase-covariant channel whose classical capacity is well known. Otherwise, we derive both a lower and an upper bound to the classical capacity of the channel, drawing inspiration from the classical treatment of the capacity of non-Gaussian additive-noise channels. We show that the lower bound to the capacity is always achievable and give examples where the non-Gaussianity of the channel can be exploited so that the communication rate beats the capacity of the Gaussian-equivalent channel (i.e. the channel where the environment state is replaced by a Gaussian state with the same covariance matrix). Finally, our upper bound leads us to formulate and investigate conjectures on the input state that minimizes the output entropy of non-Gaussian attenuator or amplifier channels. Solving these conjectures would be a main step toward accessing the capacity of a large class of non-Gaussian bosonic channels.
We derive explicit formulas for the capacity of multimode quantum Gaussian channels which serve as a fundamental model for optical version of multiple-input multiple-output channels. We show that it is always optimal to increase the number of modes under fixed power constraint. We derive an analytical formula for the ensemble-averaged Holevo capacity in the case of random passive transformations. The analogous results are also obtained for capacities achievable under homodyne and heterodyne detection. We further discuss the generalization of the model to include weak active transformations.
It is easy to show coincidence of the entanglement-assisted classical capacity and the Holevo capacity for any c-q channel between finite dimensional quantum systems. In this paper we prove the converse assertion: coincidence of the above-mentioned capacities of a quantum channel implies that the χ-essential part of this channel is a c-q channel (the χ-essential part is a restriction of a channel obtained by discarding all input states useless for transmission of classical information). The above observations are generalized to infinite dimensional quantum channels with linear constraints by using the obtained conditions for coincidence of the quantum mutual information and the constrained Holevo capacity.