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arXiv:1410.5049

Exploring maximally multipartite entanglement of even n qubits with N-tangle

Xin-Wei Zha, Jianxia Qi, Yunguang Zhang

Published Oct 19, 2014• 0 citations
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Abstract

A necessary condition of the maximally multipartite entangled states (MMES) is given via n-tangle. The condition shows that the n-tangle equal zero for the four-, and eight-qubit of MMESs and the n-tangle equal 1 for two- and six- qubits of MMESs. Furthermore,we give the theoretical limitation for maximally ten-qubit and twelve-qubit entangled states. We conjecture that 4n-qubit states of MMES should have n-tangle equal zero and 4n+2-qubit states of MMES should have n-tangle equal one.

DOI
10.48550/arxiv.1410.5049

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A necessary condition of the maximally multipartite entangled states (MMES) is given via n-tangle. The condition shows that the n-tangle equal zero for the four-, and eight-qubit of MMESs and the n-tangle equal 1 for two- and six- qubits of MMESs. Furthermore,we give the theoretical limitation for maximally ten-qubit and twelve-qubit entangled states. We conjecture that 4n-qubit states of MMES should have n-tangle equal zero and 4n+2-qubit states of MMES should have n-tangle equal one.
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.
We study the conditions for obtaining maximally multipartite-entangled states (MMESs) as nondegenerate eigenstates of Hamiltonians that involve only short-range interactions. We investigate small-size systems (with a number of qubits ranging from 333 to 555) and show some example Hamiltonians with MMESs as eigenstates.
Abstract The notion of a maximally entangled state depends on the measure used to give rise to a rich envision of multipartite state. Recently, Che et al presented a recurrence relation of multi-qubit states. According to this inspiration, we present an expanded recurrence relation of the maximally multipartite state. Using this expanded recurrence relation and Bell state, some new forms of the maximally four-, six-, eight-qubits states are presented. The construct of the maximally multipartite state through recurrence relationships is of great potential.