The entanglement for a two-parameter class of states in a high-dimension (m n,n≥m≥3) bipartite quantum system is discussed.The negativity (N) and the relative entropy of entanglement (Er) are calculated,and the ana...The entanglement for a two-parameter class of states in a high-dimension (m n,n≥m≥3) bipartite quantum system is discussed.The negativity (N) and the relative entropy of entanglement (Er) are calculated,and the analytic expressions are obtained.Finally the relation between the negativity and the relative entropy of entanglement is discussed.The result demonstrates that all PPT states of the two-parameter class of states are separable,and all entangled states are NPT states.Different from the 2 ? n quantum system,the negativity for a two-parameter class of states in high dimension is not always greater than or equal to the relative entropy of entanglement.The more general relation expression is mN/2≥Er.展开更多
In this paper,the authors first introduce the tree-indexed Markov chains in random environment,which takes values on a general state space.Then,they prove the existence of this stochastic process,and develop a class o...In this paper,the authors first introduce the tree-indexed Markov chains in random environment,which takes values on a general state space.Then,they prove the existence of this stochastic process,and develop a class of its equivalent forms.Based on this property,some strong limit theorems including conditional entropy density are studied for the tree-indexed Markov chains in random environment.展开更多
基金supported by the Project of Natural Science Foundation of Jiangsu Education Bureau,China (Grant No. 09KJB140010)the Project Prepared for National Natural Science Foundation of Xuzhou Normal University (Grant No. 08XLY03)+1 种基金the Science and Technology Foundation of Hubei Educational Bureau,China (Grant No. Q20082503)the Natural Science Foundation of Xuzhou Institute of Technology, China (Grand No. XKY2008210)
文摘The entanglement for a two-parameter class of states in a high-dimension (m n,n≥m≥3) bipartite quantum system is discussed.The negativity (N) and the relative entropy of entanglement (Er) are calculated,and the analytic expressions are obtained.Finally the relation between the negativity and the relative entropy of entanglement is discussed.The result demonstrates that all PPT states of the two-parameter class of states are separable,and all entangled states are NPT states.Different from the 2 ? n quantum system,the negativity for a two-parameter class of states in high dimension is not always greater than or equal to the relative entropy of entanglement.The more general relation expression is mN/2≥Er.
基金supported by the National Natural Science Foundation of China(Nos.11571142,11971197,11601191)。
文摘In this paper,the authors first introduce the tree-indexed Markov chains in random environment,which takes values on a general state space.Then,they prove the existence of this stochastic process,and develop a class of its equivalent forms.Based on this property,some strong limit theorems including conditional entropy density are studied for the tree-indexed Markov chains in random environment.
