scholarly journals Retrieving the covariance matrix of an unknown two-mode Gaussian state by means of a reference twin beam

2016 ◽  
Vol 375 ◽  
pp. 29-33 ◽  
Author(s):  
Ievgen I. Arkhipov ◽  
Jan Peřina
Keyword(s):  
Covariance Matrix ◽  
Gaussian State ◽  
Twin Beam

scholarly journals Symplectic decomposition from submatrix determinants

2021 ◽  
Vol 477 (2255) ◽  
Author(s):  
Jason L. Pereira ◽  
Leonardo Banchi ◽  
Stefano Pirandola
Keyword(s):  
Quantum Information ◽  
Covariance Matrix ◽  
Hermitian Matrix ◽  
Gaussian State ◽  
Diagonal Form ◽  
Symplectic Transformation ◽  
Important Theorem

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.

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