Symplectic decomposition from submatrix determinants
2021 ◽
Vol 477
(2255)
◽
Keyword(s):
An important theorem in Gaussian quantum information tells us that we can diagonalize the covariance matrix of any Gaussian state via a symplectic transformation. While the diagonal form is easy to find, the process for finding the diagonalizing 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 diagonalizing symplectic from certain submatrix determinants, which could prove useful in Gaussian quantum information.
2011 ◽
Vol 09
(04)
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pp. 1081-1090
2014 ◽
Vol 21
(01n02)
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pp. 1440001
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1974 ◽
Vol 3
(4)
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pp. 343-359
1975 ◽
Vol 4
(6)
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pp. 537-554
2003 ◽
Vol 50
(6-7)
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pp. 901-913
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