Generalized Schmidt decomposition based on injective tensor norm
Abstract
We present a generalized Schmidt decomposition for a pure system with any number of two-level subsystems. The basis is symmetric under the permutation of the parties and is derived from the product state defining the injective tensor norm of the state. The largest coefficient quantifies the quantum correlation of the state. Other coefficients have a lot of information such as the unentangled particles as well as the particles whose reduced states are completely mixed. The decomposition clearly distinguishes the states entangled in inequivalent ways and have an information on the applicability to the teleportation and superdense coding when the given quantum state is used as a quantum channel.
Cite
@article{arxiv.0809.1290,
title = {Generalized Schmidt decomposition based on injective tensor norm},
author = {Levon Tamaryan and DaeKil Park and Sayatnova Tamaryan},
journal= {arXiv preprint arXiv:0809.1290},
year = {2009}
}
Comments
rewritten as a regular paper, necessary and sufficient conditions are derived for the existence of completely mixed subsystems, six possible expressions of the injective norm are written down explicitly, a reference is added