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Searching for highly entangled
multi-qubit states
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Iain Brown, Susan Stepney, Anthony Sudbery, Samuel
L. Braunstein.

Searching for highly entangled multi-qubit states.

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Journal of Physics A
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, 38, 1119-1131, 2005.

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Abstract:

We present a simple numerical optimisation procedure to search for
highly entangled states of 2, 3, 4 and 5 qubits. We develop a
computationally tractable entanglement measure based on the negative
partial transpose (NPT) criterion, which can be applied to quantum
systems of an arbitrary number of qubits. The search algorithm attempts
to optimise this entanglement cost function to find the maximal
entanglement in a quantum system.

We present highly entangled 4 qubit and 5 qubit states discovered by
this search. We show that the 4 qubit state is not quite as entangled,
according to two separate measures, as the conjectured maximally
entangled Higuchi-Sudbery state. Using this measure, these states are
more highly entangled than the 4-qubit and 5-qubit GHZ states.

We also present a conjecture about the NPT measure, inspired by some
of our numerical results, that the single-qubit reduced states of
maximally entangled states are all totally mixed.

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Full paper
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:
PDF
216K [
Note: There is a typo in eqn.(24) on
p.13: the first three-qubit ket on the right-hand side, given as |000>,
should be |001>. This is clear from symmetry considerations: the four
three-qubit states are symmetrically disposed on the unit cube.
]

doi:
10.1088/0305-4470/38/5/013

@article(SS-JPhysA-05,
author = "Iain Brown and Susan Stepney and Anthony Sudbery and Samuel L. Braunstein",
title = "Searching for multi-qubit entanglement",
journal = "Journal of Physics A: Mathematical and General",
volume = 38,
pages = "1119-1131",
year = 2005
)