Symplectic decomposition from submatrix determinants
Abstract
An important theorem in Gaussian quantum information tells us that we can diagonalise the covariance matrix of any Gaussian state via a symplectic transformation. Whilst the diagonal form is easy to find, the process for finding the diagonalising symplectic can be more difficult, and a common, existing method requires taking matrix powers, which can be demanding analytically. Inspired by a recently presented technique for finding the eigenvectors of a Hermitian matrix from certain submatrix eigenvalues, we derive a similar method for finding the diagonalising symplectic from certain submatrix determinants, which could prove useful in Gaussian quantum information.
Cite
@article{arxiv.2108.05364,
title = {Symplectic decomposition from submatrix determinants},
author = {Jason L. Pereira and Leonardo Banchi and Stefano Pirandola},
journal= {arXiv preprint arXiv:2108.05364},
year = {2021}
}
Comments
10 pages, supplementary files available at https://github.com/softquanta/symplectic_decomposition