IQI Weekly Seminar
** Note Special time and location for this talk only - Annenberg 213, 12 noon - lunch following the talk **
Abstract: Lower bounds to the optimal error probability when coding over a classical-quantum channel have been obtained by Winter [PhD Thesis, arXiv:quant-ph/9907077] and Dalai [IEEE Trans.~Inf.~Theory, 59(12):8027--8056, 2013]. These bounds coincide in classical channels and are thus called the sphere-packing bound. In this talk, we first show that these two expressions admit a variational representation and are related by the Golden-Thompson inequality, reaffirming that Dalai's expression is stronger in general classical-quantum channels. We then establish a refined sphere-packing bound with a finite blocklength, which significantly improves the pre-factor from the order of the subexponential in Dalai's result to the polynomial.
The established refinement leads to an substantial application in moderate deviation analysis. Specifically, we show that the reliable communication through a classical-quantum channel is possible when the transmission rate approaches channel capacity slowly. This scenario exists between the non-vanishing error probability regime, where the rate tends to capacity with a fixed error, and the small error probability regime, where the error vanishes given a rate below capacity. Our approaches rely on a sharp concentration inequality in strong large deviation theory and crucial properties of the error-exponent function.