Yongsheng Yao

In their seminal work, Bennett et al. [IEEE Trans. Inf. Theory (2002)] showed that, with sufficient shared randomness, one noisy channel can simulate another at a rate equal to the ratio of their capacities. We establish that when coding above this channel interconversion capacity, the exact strong converse exponent is characterized by a simple optimization involving the difference of the corresponding Renyi channel capacities with Holder dual parameters. We extend this result to the entanglement-assisted interconversion of classical-quantum channels, showing that the strong converse exponent is likewise determined by differences of sandwiched Renyi channel capacities. The converse bound is obtained by relaxing to non-signaling assisted codes and applying Holder duality together with the data processing inequality for Renyi divergences. Achievability is proven by concatenating refined channel coding and simulation protocols that go beyond first-order capacities, achieving exponentially small conversion errors.

We provide the sandwiched Renyi divergence of order alphaın(1/2,1), as well as its induced quantum information quantities, with an operational interpretation in the characterization of the exact strong converse exponents of quantum tasks. Specifically, we consider (a) smoothing of the max-relative entropy, (b) quantum privacy amplification, and (c) quantum information decoupling. We solve the problem of determining the exact strong converse exponents for these three tasks, with the performance being measured by the fidelity or purified distance. The results are given in terms of the sandwiched Renyi divergence of order alphaın(1/2,1), and its induced quantum Renyi conditional entropy and quantum Renyi mutual information. This is the first time to find the precise operational meaning for the sandwiched Renyi divergence with Renyi parameter in the interval alphaın(1/2,1).