One-Shot Triple-Resource Trade-Off in Quantum Channel Coding

We analyze a task in which classical and quantum messages are simultaneously communicated via noisy channel, assisted with limited amount of shared entanglement. derive direct converse bounds for the one-shot capacity region, represented by smooth conditional entropies error tolerance. The proof is based on randomized partial decoupling theorem, generalization theorem. two match asymptotic limit infinitely many uses memoryless channel coincide previous result obtained Hsieh Wilde. Direct various communication tasks as corollaries, both scenarios.