The Masking Of Quantum States In Two-Dimensional Hilbert Space

In quantum mechanics,quantum information refers to the physical information of the "state" of a quantum system.Quantum communication is a new way of information for computing,encoding and information transmission through various coherent characteristics of quantum systems(such as quantum parallel,quantum entanglement and quantum no-cloning,etc.).In today’s information age of rapid development of science and technology,how to make information more secure and effective transmission has attracted more and more people’s attention.Based on the unique linear and unitary properties of closed quantum systems,quantum information masking technology arises.In 2018,Modi et al.(2018 Phys.Rev.Lett.120 230501)gave the definition of quantum information masking and reached the no-masking theorem that it is not possible to mask all arbitrary pure states with the same unitary operator.Based on this conclusion,this thesis aims to study the masking of quantum states in two-dimensional Hilbert space.The main research contents are as follows.Based on the masking condition given in the definition of quantum information masking,we study quantum information masking in two-dimensional Hilbert space.First,a system of equations as the condition of quantum information masking is proposed.It is shown that quantum information contained in a single qubit state can be masked,if and only if the coefficients of the quantum state satisfy the given system of equations.Second,by observing the characteristics of non-orthogonal maskable quantum states,we obtain a related conclusion,namely,if two non-orthogonal two-qubit quantum states can mask a single qubit state,they have the same number of terms and the same basis.Finally,for maskable orthogonal quantum states,we analyze two special examples and give their images for an intuitive description.Based on the necessary condition of the precision to make the approximate quantum information masking possible derived by Li and Modi(2020 Phys.Rev.A102 022418),we use two methods to improve the lower bound for the original precision.The improved lower bound is much tighter than the one obtained by Li and Modi.Furthermore,the improved lower bound is able to achieve approximate quantum information masking with higher fidelity.Finally,the difference between the improved lower bound and the corresponding fidelity and the results obtained by Li and Modi are compared by images.