Dresden 2011 – wissenschaftliches Programm
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Q: Fachverband Quantenoptik und Photonik
Q 12: Quantum Information: Concepts and Methods 2
Q 12.5: Vortrag
Montag, 14. März 2011, 15:30–15:45, SCH A118
Polynomial invariants for discrimination and classification of four-qubit entanglement — •Oliver Viehmann1, Christopher Eltschka2, and Jens Siewert3,4 — 1Physics Department, ASC, and CeNS, Ludwig-Maximilians-Universität, München, Germany — 2Institut für Theoretische Physik, Universität Regensburg, Regensburg, Germany — 3Departamento de Química Física, Universidad del País Vasco – Euskal Herriko Unibertsitatea, Bilbao, Spain — 4Ikerbasque, Basque Foundation for Science, Bilbao, Spain
It is well known that the number of entanglement classes in SLOCC (stochastic local operations and classical communication) classifications increases with the number of qubits and is already infinite for four qubits [1]. Bearing in mind the rapid evolution of experimental technology, criteria for explicitly discriminating and classifying pure states of four and more qubits are highly desirable and therefore in the focus of intense theoretical research.
We develop a general criterion for the discrimination of pure N-partite entangled states in terms of polynomial SL(d, ℂ )⊗ N invariants. By means of this criterion, existing SLOCC classifications of four-qubit entanglement are reproduced. Based on this we propose a polynomial classification scheme in which families are identified through “tangle patterns”, thus bringing together qualitative and quantitative description of entanglement.
[1] W. Dür, G. Vidal, and J.I. Cirac, Phys. Rev. A 62, 062314 (2000).