Unified approach to quantum capacities: Towards quantum noisy coding theorem

Based on a unified approach to all kinds of quantum capacities we show that the rate of quantum information transmission is bounded by the maximal att ainable rate of coherent information. Moreover, we show that if for any bip artite state the one-way distillable entanglement is no less than coherent information, then one obtains Shannon-like formulas for all the capacities. The inequality also implies that the decrease of distillable entanglement due to the mixing process does not exceed that of the corresponding loss of information about a system.