Highly entangled multi-qubit states with simple algebraic structure.

Recent works by
Brown
*
et al
*
(2005 J.
Phys. A: Math. Gen.
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38
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1119)
and Borras
*
et al
*
(2007 J. Phys. A: Math. Theor.
**
40
**
13407) have explored numerical
optimization procedures to search for highly entangled multi-qubit
states according to some computationally tractable entanglement measure.
We present an alternative scheme based upon the idea of searching for
states having not only high entanglement but also simple algebraic
structure. We report results for 4, 5, 6, 7 and 8 qubits discovered by
this approach, showing that
*
many
*
of such states do exist. In
particular, we find a maximally entangled 6-qubit state with an
algebraic structure simpler than the best results known so far. For the
case of 7 qubits, we discover states with high, but not maximum,
entanglement and simple structure, as well as other desirable
properties. Some preliminary results are shown for the case of 8 qubits.

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Full paper
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:
PDF
184K | doi:
10.1088/1751-8113/42/41/415301

@article(SS-JPhysA-09, author = "Juan E. Tapiador and J. C. Hernandez-Castro and John A. Clark and Susan Stepney", title = "Highly entangled multi-qubit states with simple algebraic structure", journal = "Journal of Physics A: Mathematical and Theoretical", volume = 42, pages = "415301", year = 2009 )