Information-theoretic measure of genuine multiqubit entanglement (5 pages)

Z. Chen

Jianming Cai, Zheng-Wei Zhou, Xingxiang Zhou +1 more

We consider pure quantum states of $N$ qubits and study the genuine $N$-qubit entanglement that is shared among all the $N$ qubits. We introduce an information-theoretic measure of genuine $N$-qubit entanglement based on bipartite partitions. When $N$ is an even number, this measure is presented in a simple formula, which depends only on the purities of the partially reduced density matrices. It can be easily computed theoretically and measured experimentally. When $N$ is an odd number, the measure can also be obtained in principle.

Lin Chen, Yi-Xin Chen

We introduce a feasible method of constructing the entanglement witness that detects genuine multiqubit entanglement in the vicinity of a given pure multiqubit state. We illustrate our method in the scenario of constructing the witnesses for the multiqubit states that are most often investigated theoretically and experimentally. It is shown that our method can construct the effective witnesses for experiments. We also investigate the entanglement detection of symmetric states and mixed states.

H. S. Song, Chang‐shui Yu

Gerardo Adesso, Fabrizio Illuminati

Zhong‐Xiao Man, Yun‐Jie Xia, Nguyen Ba An

We construct a genuine $(2N+1)$-qubit entangled state to perform controlled teleportation of an arbitrary $N$-qubit state. The constructed state is a complementarity to the genuine $2N$-qubit entangled state constructed by Yeo and Chua for $N=2$ [Phys. Rev. Lett. 96, 060502 (2006)] and by Chen, Zhu, and Guo for any $N$ [Phys. Rev. A 74, 032324 (2006)]. We also quantify the entanglement of the state and classify it with the well-known $GHZ$ and $W$ states by means of the recently proposed generalized global entanglement and the associated auxiliary measures [Phys. Rev. A 74, 022314 (2006)]. Our study is of general importance with respect to exploring and exploiting the genuine multiqubit entanglement.