Quantum capacity analysis of multi-level amplitude damping channels

Evaluating capacities of quantum channels is the first purpose of quantum Shannon theory, but in most cases the task proves to be very hard. Here, we introduce the set of Multi-level Amplitude Damping quantum channels as a generalization of the standard qubit Amplitude Damping Channel to quantum systems of finite dimension d. In the special case of d=3, by exploiting degradability, data-processing inequalities, and channel isomorphism, we compute the associated quantum and private classical capacities for a rather wide class of maps, extending the set of models whose capacity can be computed known so far. We proceed then to the evaluation of the entanglement assisted quantum and classical capacities. Estimating the capacity of quantum channels is relevant to understand at which rate quantum information can be exchanged. Here, the authors introduce multi-level amplitude damping channels that generalize the qubit amplitude damping noise model, analyse their quantum and private capacities, and exactly derive the capacities of quantum channels that are not anti-degradable.

Automated summary

This article introduces multi-level amplitude damping channels that generalize concepts in quantum information theory to finite-dimensional quantum systems, and computes the quantum and private classical capacities associated with these channels. By exploiting degradability, data-processing inequalities, and channel isomorphism, the authors extend the set of models whose capacity can be computed known so far.