The Theoretical Study On Three-Party Communication Complexity With Entanglement State

Quantum entanglement is the most important resource in quantum information and has many applications including quantum computing, quantum teleportation, super-dense coding and quantum cryptography. Recently, researchers found that entanglement can be used to reduce the communication complexity for a certain Boolean function. This paper shows a two-party communication complexity scenario for a certain Boolean function and gets the successful probability with or without entanglement to learn the outcome of the Boolean function. Then we propose a three-party communication complexity scenario with a general three-qubit entanglement for a certain Boolean function, whose input data are distributed in three parties. Without pre-shared entanglement, at least four bits communications are needed to accomplish the calculation task. We prove that pre-shared entanglement can reduce communication complexity to three bits with probability of success which depends on the characterization of entanglement and can reach 1 maximally. At last, we design a quantum circuit of realizing three-party communication complexity scenario with a general three-qubit entanglement.