Multi-mode entangled states represented as Grassmannian polynomials

Multi-mode entangled states represented as Grassmannian polynomials We introduce generalized Grassmannian representatives of multi-mode state vectors. By implementing the fundamental properties of Grassmann coherent states, we map the Hilbert space of the finite-dimensional multi-mode states to the space of some Grassmannian polynomial functions. These Grassmannian polynomials form a well-defined space in the framework of Grassmann variables; namely Grassmannian representative space. Therefore, a quantum state can be uniquely defined and determined by an element of Grassmannian representative space. Furthermore, the Grassmannian representatives of some maximally entangled states are considered, and it is shown that there is a tight connection between the entanglement of the states and their Grassmannian representatives. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Quantum Information Processing Springer Journals

Multi-mode entangled states represented as Grassmannian polynomials

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Publisher
Springer US
Copyright
Copyright © 2016 by Springer Science+Business Media New York
Subject
Physics; Quantum Information Technology, Spintronics; Quantum Computing; Data Structures, Cryptology and Information Theory; Quantum Physics; Mathematical Physics
ISSN
1570-0755
eISSN
1573-1332
D.O.I.
10.1007/s11128-016-1357-1
Publisher site
See Article on Publisher Site

Abstract

We introduce generalized Grassmannian representatives of multi-mode state vectors. By implementing the fundamental properties of Grassmann coherent states, we map the Hilbert space of the finite-dimensional multi-mode states to the space of some Grassmannian polynomial functions. These Grassmannian polynomials form a well-defined space in the framework of Grassmann variables; namely Grassmannian representative space. Therefore, a quantum state can be uniquely defined and determined by an element of Grassmannian representative space. Furthermore, the Grassmannian representatives of some maximally entangled states are considered, and it is shown that there is a tight connection between the entanglement of the states and their Grassmannian representatives.

Journal

Quantum Information ProcessingSpringer Journals

Published: Jun 14, 2016

References

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