Symplectic analogs of polar decomposition and their applications to bosonic Gaussian channels

Abstract

We obtain several analogs of real polar decomposition for even dimensional matrices. In particular, we decompose a non-degenerate matrix as a product of a Hamiltonian and an anti-symplectic matrix and under additional requirements we decompose a matrix as a skew-Hamiltonian and a symplectic matrix. We apply our results to study bosonic Gaussian channels up to inhomogeneous symplectic transforms.

References in corpus (3)

• Multi-mode bosonic Gaussian channels
• Not-so-normal mode decomposition
• On quantum Gaussian optimizers conjecture in the case q=p