In this paper, we present a game of dice that combines multi-party communication with a tangible interface. The game has been used as a testbed to study typical conversational behavior patterns in interactions between human users and synthetic agents. In particular, we were interested in the question to what extent the interaction with the agent can be considered as natural. As an evaluation criterion, we propose to investigate whether the communicative behaviors of humans differ when conversing with an agent as opposed to conversing with other humans.

There exist some results showing that quantum communications are more powerful than classical communications. Moreover, although quantum entangled states do not give extra information, by using prior entanglement the quantum communication complexity of some functions is less than the classical communication complexity. The communications with prior entanglement can be regarded as a type of public coin models. In this paper, we investigate quantum communications for multi-party with prior entanglement, and show that there exists a generalized inner product function for k-party such that the quantum communication complexity is at most k bits, but the classical communication complexity needs at least 3k/2 bits. Moreover, we also provide a generalized form of prior entanglements that is effective in order to compute some type of Boolean functions.