Capacity Estimates via comparison with TRO channels

Abstract: A ternary ring of operators (TRO) in finite dimensions is a diagonal sum of spaces of rectangular matrices. TRO as operator space corresponds to quantum channels that are diagonal sums of partial traces, which we call TRO channels. TRO channels admits simple, single-letter capacity formula. Using operator space and complex interpolation techniques, we give perturbative capacities estimates for a wider class of quantum channels by comparison to TRO channels. Our estimates applies mainly for quantum and private capacity and also strong converse rates. The examples includes random unitary from group representations which in general are non-degradable channels.