Quantum communication THEORY

Quantum capacity of a noisy quantum channel is a fundamental quantity that quantifies the maximum number of quantum bits (per channel use) that can be transmitted faithfully through the noisy channel upon an optimal quantum error correction scheme. Gaussian thermal loss channels model energy loss and gain errors in realistic optical communication channels and microwave cavity modes. Thus, evaluation of the quantum capacity of a Gaussian thermal loss channel is of fundamental importance to the continuous-variable quantum information processing.

The best known lower bound of the Gaussian thermal loss channel capacity was its coherent information with respect to an input single-mode thermal state, or an uncorrelated multi-mode thermal state. We found that sometimes correlated multi-mode thermal states can outperform the single-mode thermal state subject to the same average photon number constraint and thus established an improved lower bound of the Gaussian thermal loss channel capacity. By doing so, we established the superadditivity of Gaussian thermal loss channels with respect to Gaussian input states.

In addition to (heuristically) showing that the hexagonal-lattice GKP code is the optimal single-mode bosonic code for Gaussian thermal loss channels, we also proved that a family of multi-mode GKP codes (defined over an optimal symplectic lattice) achieves the quantum capacity of Gaussian thermal loss channels up to at most a constant number (~log_{2}e = 1.44...) of qubits per channel use.