The Universal Unambiguous Discriminator Between Two Unknown Qudit States

In quantum computing and quantum information,it is inevitable to encounter the problem of information acquisition.Quantum state discrimination,as an important method to obtain information,is an essential content in quantum computation and quantum information.If the state of a quantum system is one of a set of quantum states,how can we determine the state of the quantum system by means of quantum mechanics?This is the task of quantum state discrimination.According to the quantum mechanics,we know that non-orthogonal quantum states are impossible to be accurately distinguished.So,how can we design a quantum measurement to distinguish two non-orthogonal quantum states in an optimal way?Therefore,the problem of quantum state discrimination is an important problem.In the thesis,we mainly study the programmable quantum state discrimination between two states in d-dimensional Hilbert space.First,we briefly introduce the basic knowledge related to quantum state discrimination.Then,we analyze the universal programmable discriminator proposed by Bergou and Hillery,which can unambiguously distinguish two unknown states in 2dimensional Hilbert space.Next,we discuss the generalized case where the states is in an ddimensional(d≥2)Hilbert space.According to the symmetry properties of the total quantum states in some particular subspaces,the Hilbert space H(?)3 of the total quantum states is decomposed as a direct sum of a series of subspaces.In subspace,according to the symmetry properties mentioned above and in combination with Neumark’s theorem,one can unambiguously discriminate between the part of the quantum state projected on the subspace.Thus,the programmable discrimination of unknown quantum states in d-dimensional Hilbert spaces is transformed into a series discrimination between quantum states with symmetry in subspaces.By this method,we obtain the maximum probability of optimal discrimination for unknown quantum state.and the corresponding measurement operator are obtained.It is also found that the optical success probability of unambiguous discrimination for unknown pure states the dimension of the state space is independent of the dimension of the state space.