Masking Of Quantum Information

Quantum information theory extends classical information to quantum information,expresses information in quantum states,and performs various information processing tasks with the information operation allowed by the quantum mechanical system.Since the evolution in closed quantum systems is unitary and linear,there are some no-go theorems in the quantum world,such as the no-cloning theorem,the no-broadcasting theorem,and the no-deleting theorem.Recently Modi et al.proposed and proved the no-masking theorem:No masker can mask all states of qubit in the bipartite quantum systems.This is another addition to the no-go theorem.However,when more partites are involved in the masking process,it is possible to mask all the qubit states.Sometimes,in order to solve practical problems,we need more than one masking scheme,so finding masking schemes in multipartite quantum systems becomes an important research content of quantum information masking.This paper studies the masking schemes of single qubit states in the multi-qubit systems.Firstly,we give masking schemes for all single qubit states in 5-qubit and 7-qubit systems.Then we prove that all single qubit states can be masked in 2n-qubit systems,where9)?~*and9)>1.In addition,different masking schemes are given for all single qubit states in 6-qubit,8-qubit,10-qubit and 12-qubit systems.In the first chapter,we introduce the basic knowledge related to the masking of quantum information,such as quantum states,density operators and reduced density operators.In the second chapter,we give the definition of the masker and the operations of en-coding all single qubit states into 5-qubit states and 7-qubit states is defined respectively.By calculating the reduced density operators of the encoded 5-qubit and 7-qubit states,it is proved that all single qubit states can be masked in 5-qubit or 7-qubit systems.In the third chapter,first of all,we give two masking schemes for all single qubit states in 6-qubit and 8-qubit systems.Then,we prove that all single qubit states can be masked in 2n-qubit systems.Finally we give three masking schemes for all single qubit states in10-qubit systems and four masking schemes for all single qubit states in 12-qubit systems.