Negativity fonts, multiqubit invariants and four qubit maximally entangled states

Negativity fonts, multiqubit invariants and four qubit maximally entangled states Recently, we introduced negativity fonts as the basic units of multipartite entanglement in pure states. We show that the relation between global negativity of partial transpose of N−qubit state and linear entropy of reduced single qubit state yields an expression for global negativity in terms of determinants of negativity fonts. Transformation equations for determinants of negativity fonts under local unitaries (LU’s) are useful to construct LU invariants such as degree four and degree six invariants for four qubit states. The difference of squared negativity and N−tangle is an N qubit invariant which contains information on entanglement of the state caused by quantum coherences that are not annihilated by removing a single qubit. Four qubit invariants that detect the entanglement of specific parts in a four qubit state are expressed in terms of three qubit subsystem invariants. Numerical values of invariants bring out distinct features of several four qubit states which have been proposed to be the maximally entangled four qubit states. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Quantum Information Processing Springer Journals

Negativity fonts, multiqubit invariants and four qubit maximally entangled states

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Publisher
Springer US
Copyright
Copyright © 2011 by Springer Science+Business Media, LLC
Subject
Physics; Quantum Information Technology, Spintronics; Quantum Computing; Data Structures, Cryptology and Information Theory; Quantum Physics; Mathematical Physics
ISSN
1570-0755
eISSN
1573-1332
D.O.I.
10.1007/s11128-011-0324-0
Publisher site
See Article on Publisher Site

Abstract

Recently, we introduced negativity fonts as the basic units of multipartite entanglement in pure states. We show that the relation between global negativity of partial transpose of N−qubit state and linear entropy of reduced single qubit state yields an expression for global negativity in terms of determinants of negativity fonts. Transformation equations for determinants of negativity fonts under local unitaries (LU’s) are useful to construct LU invariants such as degree four and degree six invariants for four qubit states. The difference of squared negativity and N−tangle is an N qubit invariant which contains information on entanglement of the state caused by quantum coherences that are not annihilated by removing a single qubit. Four qubit invariants that detect the entanglement of specific parts in a four qubit state are expressed in terms of three qubit subsystem invariants. Numerical values of invariants bring out distinct features of several four qubit states which have been proposed to be the maximally entangled four qubit states.

Journal

Quantum Information ProcessingSpringer Journals

Published: Nov 11, 2011

References

  • Simple criteria for the SLOCC classification
    Li, D.

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