Pereira, Jason L., Banchi, Leonardo and Pirandola, Stefano orcid.org/0000-0001-6165-5615 (2021) Symplectic decomposition from submatrix determinants. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences. 20210513. ISSN 1364-5021
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.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | 8 pages, supplementary files available at https://github.com/softquanta/symplectic_decomposition This is an author-produced version of the published paper. Uploaded in accordance with the publisher’s self-archiving policy. Further copying may not be permitted; contact the publisher for details |
Keywords: | math-ph,math.MP,quant-ph |
Dates: |
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Institution: | The University of York |
Academic Units: | The University of York > Faculty of Sciences (York) > Computer Science (York) |
Depositing User: | Pure (York) |
Date Deposited: | 07 Oct 2021 10:50 |
Last Modified: | 16 Oct 2024 17:54 |
Published Version: | https://doi.org/10.1098/rspa.2021.0513 |
Status: | Published |
Refereed: | Yes |
Identification Number: | 10.1098/rspa.2021.0513 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:178961 |