Communications in Theoretical Physics

Extremal Entangled Four-Qubit Pure States with Respect to Multiple Entropy Measures

Dan Liu, Zhao Xin, Long Gui-Lu

Published Feb 1, 2008• 13 citations

Abstract

Four-qubit entanglement has been investigated using a recent proposed entanglement measure, multiple entropy measures (MEMS). We have performed optimization for the nine different families of states of four-qubit system. Some extremal entangled states have been found.

DOI: 10.1088/0253-6102/49/2/16

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Communications in Theoretical Physics

Extremal Entangled Four-Qubit Pure States with Respect to Multiple Entropy Measures

Dan Liu, Zhao Xin, Long Gui-Lu

Published Feb 1, 2008• 13 citations

Publisher

Abstract

DOI: 10.1088/0253-6102/49/2/16

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A new entanglement measure, the multiple entropy measures (MEMS), is proposed to quantify quantum entanglement of multi-partite quantum state. The MEMS is vector-like with

m=[N/2]

, the integer part of

N/2

, components:

[S_1, S_2,..., S_m]

, and the

i

-th component

S_i

is the geometric mean of

i

-body partial entropy of the system. The

S_i

measures how strong an arbitrary

i

bodies from the system are entangled with the rest of the system. The MEMS is not only transparent in physical picture, but also simple to calculate. It satisfies the conditions for a good entanglement measure. We have analyzed the entanglement properties of the GHZ-state, the W-states and cluster-states under MEMS. The cluster-state is more entangled than the GHZ-state and W-state under MEMS.