Normal forms and entanglement measures for multipartite quantum states

By Frank Verstraete, Jeroen Dehaene, B. De Moor. 2001

211 citations recorded by the source corpus.

A general mathematical framework is presented to describe local equivalence classes of multipartite quantum states under the action of local unitary and local filtering operations. This yields multipartite generalizations of the singular value decomposition. The analysis naturally leads to the introduction of entanglement measures quantifying the multipartite entanglement (as generalizations of the concurrence for two qubits and the 3-tangle for three qubits), and the optimal local filtering operations maximizing these entanglement monotones are obtained. Moreover, a natural extension of the definition of Greenberger-Horne-Zeilinger states to, e.g., 2x2xN systems is obtained.

Subfields: Artificial Intelligence, Atomic and Molecular Physics, and Optics

View Paper: https://www.semanticscholar.org/paper/8c3034c8b2cec64f547d352e5f9a0874cbd9859a

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In Artificial Intelligence

In Atomic and Molecular Physics, and Optics

Citations in the corpus

Entanglement certification from theory to experiment (2018, background): “, which can be filtered to locally maximally mixed states [228], comprising all states except for a measurezero subset.”
Entanglement detection (2008, background): “where theG k are traceless orthogonal observables [171,172].”
Entanglement in many-body systems (2007, background): “The latter is the invariance group relevant for qubit entanglement classification and quantification (Dür et al., 2000; Osterloh and Siewert, 2005; Verstraete et al., 2003).”