The Kalman Decomposition for Linear Quantum Stochastic Systems
  The Kalman decomposition for Linear Quantum Stochastic Systems in the real quadrature operator representation, that was derived indirectly in [1] by the authors, is derived here directly, using the "one-sided symplectic" SVD-like factorization of [2] on the observability matrix of the system. 
Symeon Grivopoulos, Guofeng Zhang, Ian R. Petersen, John Gough
quant-ph