Property of capacity by WDM for attenuated quantum channel

In 2004, Giovannetti and others gave both the broadband and narrowband channel capacities of an attenuated quantum channel [1]. However, the derived broadband channel capacity is impossible to realize. Therefore, we treat the broadband channel capacity as an upper bound and it is necessary to derive an achievable limit. In a previous work, to show the true capacity, the capacity by wavelength division multiplexing (WDM) was defined and compared with the broadband channel capacity when there is no attenuation [7]. We consider more detailed properties of this WDM capacity and attenuated channels with frequency-dependent loss.