Multiparty Quantum Computation for Summation and Multiplication with Mutually Unbiased Bases

We present an efficient protocol to securely compute the summation and multiplication of the multiparty secure numbers via quantum states in MUBs. In our protocols, we assume the third party Alice is semi-honest which means Alice might want to steal the secret messages of the participants but cannot be corrupted by the participants. The agents use decoy photons which are randomly in one of 2dm nonorthogonal multiparticle states to prevent the eavesdropper and potential dishonest agents from freely eavesdropping on the secure information. The scheme requires the agents of computation to transmit fewer particles for multiparty summation and multiplication, which makes the scheme more convenient to use than others. Moreover, it has the advantage of having high information capacity per photon for summation and multiplication in multiparty quantum computation.