Description of quantum entanglement with nilpotent polynomials

Extensive characterization of entanglement and canonical forms

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

Research output: Chapter in Book/Report/Conference proceedingConference contribution

2 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.

Original languageEnglish
Title of host publicationProceedings of SPIE - The International Society for Optical Engineering
Volume6264
DOIs
Publication statusPublished - 2006
Externally publishedYes
EventQuantum Informatics 2005 - Moscow, Russian Federation
Duration: Oct 3 2005Oct 7 2005

Other

OtherQuantum Informatics 2005
CountryRussian Federation
CityMoscow
Period10/3/0510/7/05

Fingerprint

Quantum entanglement
canonical forms
polynomials
Polynomials
state vectors
logarithms
Mathematical operators
Vacuum
operators
vacuum

ASJC Scopus subject areas

  • Electrical and Electronic Engineering
  • Condensed Matter Physics

Cite this

Mandilara, A., Akulin, V. M., Smilga, A. V., & Viola, L. (2006). Description of quantum entanglement with nilpotent polynomials: Extensive characterization of entanglement and canonical forms. In Proceedings of SPIE - The International Society for Optical Engineering (Vol. 6264). [626402] https://doi.org/10.1117/12.683104

Description of quantum entanglement with nilpotent polynomials : Extensive characterization of entanglement and canonical forms. / Mandilara, Aikaterini; Akulin, Vladimir M.; Smilga, Andrei V.; Viola, Lorenza.

Proceedings of SPIE - The International Society for Optical Engineering. Vol. 6264 2006. 626402.

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Mandilara, A, Akulin, VM, Smilga, AV & Viola, L 2006, Description of quantum entanglement with nilpotent polynomials: Extensive characterization of entanglement and canonical forms. in Proceedings of SPIE - The International Society for Optical Engineering. vol. 6264, 626402, Quantum Informatics 2005, Moscow, Russian Federation, 10/3/05. https://doi.org/10.1117/12.683104
Mandilara A, Akulin VM, Smilga AV, Viola L. Description of quantum entanglement with nilpotent polynomials: Extensive characterization of entanglement and canonical forms. In Proceedings of SPIE - The International Society for Optical Engineering. Vol. 6264. 2006. 626402 https://doi.org/10.1117/12.683104
Mandilara, Aikaterini ; Akulin, Vladimir M. ; Smilga, Andrei V. ; Viola, Lorenza. / Description of quantum entanglement with nilpotent polynomials : Extensive characterization of entanglement and canonical forms. Proceedings of SPIE - The International Society for Optical Engineering. Vol. 6264 2006.
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