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.
The synthesis of the Toffoli gate, Fredkin gate, three-qubit Inversion-on-equality gate and D(α) gate, as well as their implementation in a three spins system coupled with Ising interaction are investigated. The sequences of the control pulse and the drift process to implement these gates are given. It is revealed that the implementation of some three-qubit gates in a circular spin chain is much better than in a linear spin chain, and every two measurements of the quantum computation complexity are not always consistent. It is significant to directly study the implementation of the multi-qubit gates and even more complicated components of quantum information processing without resorting to their synthesis.
WEI HaiRui, DI YaoMin & WANG Yan School of Physics & Electronic Engineering, Xuzhou Normal University, Xuzhou 221116, China
In this paper,we investigate the controllability of spin 1 systems and the realization of ternary gates.Using dipole and quadrupole operators as the orthogonal basis of su(3) algebra,we discuss the controllability of one spin 1 systems and offer the concept of a complete set of control operators first.Then we present the controllability of two spin 1 systems coupled with Ising interaction and the transforming relations of the drift process of the system.Finally the specific realization of the ternary SWAP gate in these systems is discussed.It takes 9 drift processes and 25 basic control processes.
