Polynomial invariants for discrimination and classification of four-qubit entanglement

Journal Article · Sun May 15 04:00:00 EDT 2011 · Physical Review. A

DOI:https://doi.org/10.1103/PHYSREVA.83.052330· OSTI ID:21546747

Viehmann, Oliver; Eltschka, Christopher; Siewert, Jens ^[1]

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1. Physics Department, Arnold Sommerfeld Center for Theoretical Physics, and Center for NanoScience, Ludwig-Maximilians-Universitaet, Theresienstrasse 37, D-80333 Muenchen (Germany)

The number of entanglement classes in stochastic local operations and classical communication (SLOCC) classifications increases with the number of qubits and is already infinite for four qubits. Criteria for explicitly discriminating and classifying pure states of four and more qubits are highly desirable and therefore at 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){sup xN} 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 entanglement types are identified through 'tangle patterns'. This scheme provides a practicable way to classify states of arbitrary multipartite systems. Moreover, the use of polynomials induces a corresponding quantification of the different types of entanglement.

• OSTI ID: 21546747
• Journal Information: Physical Review. A, Journal Name: Physical Review. A Journal Issue: 5 Vol. 83; ISSN 1050-2947; ISSN PLRAAN
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
COMMUNICATIONS
FOUR-BODY PROBLEM
FUNCTIONS
INFORMATION
MANY-BODY PROBLEM
POLYNOMIALS
PURE STATES
QUANTUM ENTANGLEMENT
QUANTUM INFORMATION
QUANTUM STATES
QUBITS
STOCHASTIC PROCESSES