Broadcasting Quantum Coherence Via Specific Quantum Operations

Quantum coherence has recently emerged as a key candidate for use as a resource in various quantum information processing tasks.One of the main problems in any quantum resource theory is the characterization of the conversions between resources by means of the free operations of the theory.In this work,we consider if coherence,already present in a reference system,can be broadcast to the auxiliary system via incoherent operations.We prove that it is impossible for a weaker form of broadcasting via incoherent operations(called weak broadcasting).This shows that broadcasting of coherence is forbidden via incoherent operations in every finitedimensional system.We obtain that coherence can be generalized broadcasting via incoherent quantum operations if and only if the quantum state in the reference system is coherent.Meanwhile,we are able to give a method for constructing an incoherent quantum operation to broadcast coherence.In addition,we prove that broadcasting of coherence is possible via a local unitary operation,but broadcasting of coherence is impossible via a direct-sum unitary operation,the quantum Fourier transformation and a unitary operation generated by a magic matrix.Furthermore,we give structure of quantum states whose coherence can be weak broadcasting and generalized broadcasting via a direct-sum unitary operation,the quantum Fourier transformation and a unitary operation generated by a magic matrix,respectively.This paper is divided into three chapters,the specific contents are as follows:In Chapter 1,we introduce some research backgrounds and status on our main contents,and review some basic concepts and existing theorems of quantum information which will be used in this paper.In Chapter 2,we propose definitions of broadcasting,weak broadcasting and generalized broadcasting quantum coherence via incoherent quantum operations.We prove broadcasting and weak broadcasting of coherence is impossible.We get some important conclusions about generalized broadcasting of quantum coherence via incoherent quantum operations.In Chapter 3,we discuss broadcasting,weak broadcasting and generalized broadcasting of quantum coherence via four special unitary operations.