Algorithmic Superactivation of Asymptotic Quantum Capacity of Zero-Capacity Quantum Channels

The superactivation of zero-capacity quantum channels makes it possible to use two zero-capacity quantum channels with a positive joint capacity for their output. Currently, we have no theoretical background to describe all possible combinations of superactive zero-capacity channels; hence, there may be many other possible combinations. In practice, to discover such superactive zero-capacity channel-pairs, we must analyze an extremely large set of possible quantum states, channel models, and channel probabilities. There is still no extremely efficient algorithmic tool for this purpose. This paper shows an efficient algorithmical method of finding such combinations. Our method can be a very valuable tool for improving the results of fault-tolerant quantum computation and possible communication techniques over very noisy quantum channels.Comment: 35 pages, 17 figures, Journal-ref: Information Sciences (Elsevier, 2012), presented in part at Quantum Information Processing 2012 (QIP2012), v2: minor changes, v3: published version; Information Sciences, Elsevier, ISSN: 0020-0255; 201

Collision Entropy Estimation in a One-Line Formula

We address the unsolved question of how best to estimate the collision entropy, also called quadratic or second order Rényi entropy. Integer-order Rényi entropies are synthetic indices useful for the characterization of probability distributions. In recent decades, numerous studies have been conducted to arrive at their valid estimates starting from experimental data, so to derive suitable classification methods for the underlying processes, but optimal solutions have not been reached yet. Limited to the estimation of collision entropy, a one-line formula is presented here. The results of some specific Monte Carlo experiments give evidence of the validity of this estimator even for the very low densities of the data spread in high-dimensional sample spaces. The method strengths are unbiased consistency, generality and minimum computational cost