Communication Complexity of Entanglement-Assisted Multi-Party Computation

We consider a quantum and a classical version of a multi-party function computation problem with <i>n</i> players, where players 2,…,n need to communicate appropriate information to player 1 so that a "generalized" inner product function with an appropriate promise can be calculated. In the quantum version of the protocol, the players have access to entangled qudits but the communication is still classical. The communication complexity of a given protocol is the total number of classical bits that need to be communicated. When <i>n</i> is prime, and for our chosen function, we exhibit a quantum protocol (with complexity (n-1)(logn) bits) and a classical protocol (with complexity ((n-1)2(logn2) bits)). Furthermore, we present an integer linear programming formulation for determining a lower bound on the classical communication complexity. This demonstrates that our quantum protocol is strictly better than classical protocols.