Quantum entanglement via nilpotent polynomials

Aikaterini Mandilara, Vladimir M. Akulin, Andrei V. Smilga, Lorenza Viola

Research output: Contribution to journalArticlepeer-review

23 Citations (Scopus)

Abstract

We propose a general method for introducing extensive characteristics of quantum entanglement. The method relies on polynomials of nilpotent raising operators that create entangled states acting on a reference vacuum state. By introducing the notion of tanglemeter, the logarithm of the state vector represented in a special canonical form and expressed via polynomials of nilpotent variables, we show how this description provides a simple criterion for entanglement as well as a universal method for constructing the invariants characterizing entanglement. We compare the existing measures and classes of entanglement with those emerging from our approach. We derive the equation of motion for the tanglemeter and, in representative examples of up to four-qubit systems, show how the known classes appear in a natural way within our framework. We extend our approach to qutrits and higher-dimensional systems, and make contact with the recently introduced idea of generalized entanglement. Possible future developments and applications of the method are discussed.

Original languageEnglish
Article number022331
JournalPhysical Review A - Atomic, Molecular, and Optical Physics
Volume74
Issue number2
DOIs
Publication statusPublished - 2006

ASJC Scopus subject areas

  • Atomic and Molecular Physics, and Optics

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