Entanglement Criterion of N-Qubit State

Thierry Bastin, Stéphanie Krins, Pierre Mathonet +3 more

Xin-Wei Zha, Hai-Yang Song, Feng Feng

Paolo Facchi, et al. [ Phys. Rev. A 77 (2008) 060304(R) ] presented a maximally multipartite entangled state (MMES). Here, we give a criterion for the identification of maximally entangled four-qubit states. Using this criterion, we not only identify some existing maximally entangled four-qubit states in the literature, but also find several new maximally entangled four-qubit states as well.

Xiaoyu Chen, Li-zhen Jiang

Starting from explicitly constructing an entanglement witness for the mixture of a Dicke state with white noise (noisy Dicke state), we provide an entanglement criterion for any multiqubit state. The criterion is necessary and sufficient for noisy $W$ states of three, four, and five qubits. We demonstrate an entanglement criterion for any four-qubit state. The criterion is necessary and sufficient for the generalized noisy four-qubit Dicke states. We present the sufficient criterion of full separability for a noisy $2k$ qubit Dicke state with $k$ excitations. Then we generalize the entanglement witness and criterion to the mixture of white noise and generic $n$-qubit Dicke state with $k$ excitations based on strong numeric evidence. Apart from noisy Dicke states, we also consider the entanglement properties of simultaneously amplitude damped and dephased Dicke states, and depolarized multiqubit $W$ states.

Renán Cabrera, W. E. Baylis

Xin-Wei Zha, Chenzhi Yuan, Yanpeng Zhang

We first present a generalized criterion for maximally entangled states of 2–8 and in theory to arbitrary-number qubits. By this criterion, some known highly entangled multi-qubit states are examined and a new genuine eight-qubit maximally entangled state is obtained. For the four-, seven- and eight-qubit system in which no perfect maximally multi-qubit entangled state (MMES) was thought to exist before, we find that the proven four- and eight-qubit MMESs and the suspected seven-qubit MMES, are not completely mixed in subsystems with two, four and three qubits, respectively, but are completely mixed in subsystems with fewer qubits. The new criterion and MMES can play important roles in quantum information technology, such as teleportation and dense coding.

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