Abstract
Quantum entropy inequalities are studied. Some quantum entropy inequalities are obtained by several methods. For an entanglement breaking channel, we show that the entanglement-assisted classical capacity is upper bounded by log d. A relationship between entanglement-assisted and one-shot unassisted capacities is obtained. This relationship shows the entanglement-assisted channel capacity is upper bounded by the sum of log d and the one-shot unassisted classical capacity.
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