GaussianStates.jl

This is the documentation for the GaussianStates.jl package.

The package defines several Gaussian maps that can be applied to Gaussian states, as well as relevant matrix decompositions.

This package mostly follows the notation in [1], with first and second moments $R_i$ and $\sigma_{ij}$ defined as

\[\begin{align} R_i &= \operatorname{tr}(\rho r_i)\\ \sigma_{ij} &= \operatorname{tr}(\rho \{r_i-R_i,r_j-R_j\}) =\\ &= \operatorname{tr}(\rho \{r_i,r_j\})-2R_iR_j, \end{align}\]

where $r = (x_1, p_1, x_2, p_2, \dotsc, x_n, p_n)$.

Package features

• Creation of vacuum, thermal, and random Gaussian states.
• Most of the Gaussian operations listed in [2].
• Williamson, Takagi-Autonne, and Euler/Bloch-Messiah matrix decompositions.

Bibliography