Quantum State Representation Based On Star-relevant Graph And Its Application

Quantum state,as the basic concept of quantum computing,have distinc-tive and rich mathematic structures and physic properties,i.e.,superposition and entanglement etc.The quantum no-cloning theorem,which is derived from the superposition of quantum state,can be used to devise the quantum cryp-tography protocols,i.e.,QKD,QSS.Quantum computation,which is based on the entanglement and superposition of quantum state,can be used to construct quantum algorithms,i.e.,Shor's algorithm,Grover algorithm.Also,Von neu-mann entropy,separability and LOCC can be used to characterize the property of quantum state.In this paper,based on the star-relevant graph,we investigate the corre-sponding quantum state and then the relationship between the graph operation and Von Neumann entropy,LOCC,1.Based on the correspondence between the eigenvalue of Laplacian matrix and quantum state of star-relevant graph,we present the specific quantum state,which corresponding to star-like,star-alike and star-mlike graph;2.The graph operation,adding an edge on star-relevant graph,will increase the Von Neumann entropy.Fixed the edge number,we provide the Von Neumann entropy rule for different star-relevant graphs;3.Based on the Neislen's theorem,the graph operation,adding an edge on star-relevant graph,cannot simulated by LOCC under certain condition;4.Under the unit module complex weighted graph condition,discussed the situation when should the star-relevant graph as quantum representation.Also,we provide an example to illustrate that certain graph operation can be simulated by LOCC.As for the star graph union ring condition,we investigate the relationship be-tween graph operation,adding peripheral edge on vertices of star graph,and Von Neumann entropy,LOCC.Finally,we make the conclusion and present several conjectures for future work.