Optimizing the fundamental limits for quantum and private communication
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The quantum capacity of a noisy quantum channel determines the maximal rate at which we can code reliably over asymptotically many uses of the channel, and it characterizes the channel's ultimate ability to transmit quantum information coherently. In this paper, we derive single-letter computable upper bounds on the quantum and private capacities of quantum channels. The quantum capacity of a quantum channel is always no larger than the quantum capacity of its extended channels, such as its flagged channel, since the flags (or extensions) of the channel can be considered as assistance from the environment. By optimizing the degrading channel of the flagged quantum channel as well as the parametrized flag states, we obtain new upper bounds on the quantum capacity of the main channel. Furthermore, we generalize our approach to private communication and derive upper bounds on the private classical capacity of a quantum channel. As notable applications, we establish improved upper bounds to the quantum and private capacities for fundamental quantum channels of great interest in quantum information, some of which are also the sources of noise in superconducting quantum computing. In particular, our upper bounds on the quantum capacities of the depolarizing channel and the generalized amplitude damping channel are strictly better than previously best-known bounds.
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