Masking Quantum Information Encoded In Pure And Mixed States

Masking of quantum information means that information is hidden from a subsystem and spread over a composite system.Modi et al.proved in[Phys.Rev.Lett.120,230501(2018)]that this is true for some restricted sets of nonorthogonal quantum states.In this paper,we discuss the problem of masking quantum information encoded in pure and mixed states,respectively.Based on an established necessary and sufficient condition for a set of pure states to be masked by an operator,we find that there exists a set of four states that can not be masked,which implies that to mask unknown pure states is impossible.We construct a masker S#and obtain its maximal maskable set,leading to an affirmative answer to a conjecture proposed in Modi's paper mentioned above.We also prove that an orthogonal(resp.linearly independent)subset of pure states can be masked by an isometry(resp.injection).This article is based on approximate masking and probability masking encoded in pure states in[arXiv:1912.02419vl(2019)]by Li M.S.and Modi K.Some definitions and theorems have been further perfected and rewritten,giving the complete definition and complete proofs of related theorems of ?-approximate masking and?-approximate probability masking encoded in pure state.Generalizing the case of pure states,we introduce the maskability of a set of mixed states and prove that a commuting subset of mixed states can be masked by an isometry S? while it is impossible to mask all of mixed states by any operator.We also find the maximal maskable sets of mixed states of the isometries S#and S?,respectively.The first chapter introduces the related research background and previous research results.The second chapter introduces the definition of masking quantum information encoded in pure states,and studies the related theorems of masking quantum information encoded in pure states.In addition,some definitions and related theorems of approximate masking and probability masking encoded in pure states are given.In the third chapter,we introduce the definition of masking quantum information encoded in mixed states,and studies the related theorems of masking quantum information encoded in mixed states.