Information complexity (IC) was introduced around 2000 to study communication complexity (CC) and it turns out to be one of the most powerful methods. Many elegant message-compression algorithms have been discovered to compress protocols with low IC since then. After quantum information complexity (QIC) was defined by Touchette in 2014, It is interesting to ask whether we are able to compress quantum protocols with low QIC via quantizing those classical message-compression algorithms. In this talk, I will survey some recent results towards the direction in several different communication complexity settings.
