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arXiv · 1909.00838

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

A. E. Teretenkov
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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.

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A. E. Teretenkov. 2019-09-02. Symplectic analogs of polar decomposition and their applications to bosonic Gaussian channels. https://doi.org/10.1080/03081087.2020.1771253

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