Research On The Multi-party Computation And The Quantum Detection Of Optical Coherent State Signal

In the researching area of the quantum communication complexity, there is increasing endeavour in the researching of the communication complexity of the multi-party computation. Besides, in the area of the quantum detection of the optical coherent state, there has been much research conclusion for the Minimum Error Discrimination(MED) measurement, while the research for the unambiguous state discrimination(USD) has just yet to begin. Based on these situations in the quantum communication fields, we propose the considering analysis and investigate, and have got the following innovative achievements:(1) We first investigate on the Multi-party Date Problem(MPD) to analyze its classical communication complexity, then the quantum distributed algorithm is constructed, and the quantum communication complexity for MPD is presented. It has been proved that the quantum algorithm degrade the communication complexity by a quadratic order than the classical case. The performance analysis examined the advantage of quantum algorithm against the classical circumstances, and when the problem is concerning about a large user number, this priviledge is of more evidence.(2) The classical communication complexity of the Multi-Party Computation(MPC) based on the discriminant function is studied, and the quantum distributed algorithm for the MPC problem is proposed. The solution shows that the performance of the quantum algorithm relies on the difference of the order of the infinity between the square root of the function definition domain and the user number. It can be concluded that the quantum communication complexity will decrease at a nearly quadratic level than the classical method.(3) The estimation of the number of solution for the MPC problem based on the discriminant function and the MPD problem is studied, and the estimation algorithm for the solution number is presented. As for the MPC problem, employ the quantum phase estimation algorithm for the estimation of the number of the solution will result in an equivalent communication complexity with that of the quantum distributed algorithm. While for the MPD problem, the solution number can be estimated with an approaching efficiency of the phase estimation algorithm without any communication. The simulation afterwards verified the efficiency.(4) The USD measurement for the On-Off Keying(OOK) modulation of the coherent state signal is explored, and the formula of the deterministic as well as the error probability of it in the presence of the thermal noise field is presented. Considering the symmetry character of the coherent state, we investigate on USD measurement of the coherent state signal with the Binary-Phase-Shift Keying(BPSK) modulation and the Quadrature-Phase-Shift Keying(QPSK) modulation, and also the deterministic and the error probability formula in the presence of the thermal noise of them are deduced respectively. The result shows that, because of the presence of the thermal noise fields, the optimal USD measurement has degenerated to a general quantum measurement, therefore it’s beyond the reality to implement the ideal USD measurement, as the average photon number of the thermal noise field has decided the distance that the USD measurement deviate from the ideal circumstances.(5) A multiple access channel model based on the symmetric coherent state is studied, and the analytical formula of the average interference of users is presented. Also with this model, the multi user detection method with the USD measurement is proposed, and the analytical formula of the detection error probability of the users is presented. The result implicats that compared with the situation that the error occur with the MED measurement, employing the ideal USD measurement will achieve the free-error discrimination for the different users.(6) We further investigated on the two access channel model based on the symmetric coherent state, with which we proposed the error probability of user detection and the max channel capacity formula for the MED measurement and USD measurement restectively. The result shows that the USD measurement can discriminate between different users with no error, but the max channel capacity of it is less than the MED measurement. Besides, the formula of the error probability of user detection and the max channel capacity with the USD measurement in the presence of thermal noise field are deducted. The conclusion shows that, while the average photon number of thermal noise field increases from 0, the error probability of user detection with the USD measurement will also increase from free error, and the max channel capacity will decrease from the case of the noise absence state accordingly.The research on the MPD and MPC problem has established that the quantum distributed algorithm can reduce the multi-party communication costs efficiently. Besides, the USD measurement of the coherent state signal in the presence of the thermol noise has enriched the quantum detection theory of the coherent state signal, and the quantum detection method of multy user with the USD measurement has superiority in the efficiency than the MED method. These achievements contribute to both the theoretic and the application developing of the optical quantum communication technology significantly.