Abstract
This thesis concerns the quantum detection problem for ternary pure state signals. We first review the relevant study on the quantum signal detection problem in the manner determined in Eldar's paper. We verify her result with the ternary geometrically uniform (GU) pure state signal having the uniform prior probability distribution, in which we have used the matrix-form expression of the optimum detection operators. Next, we consider the optimum detection problem for the ternary GU pure state signal under the condition that one prior probability is given and the others are unknown. In this situation, we formulate our optimization problem and derive the necessary and sufficient conditions for the solution of the problem. To seek the closed-form expression for the optimum detection operators, we perform the numerical simulation. As a result, we make a conjecture on the closed-form expression of the optimum measurement operators and on the optimum prior distribution for our problem.