Peres-Horodecki criterion systems
In continuous variable systems, the Peres-Horodecki criterion also applies. Specifically, Simon formulated a particular version of the Peres-Horodecki criterion in terms of the second-order moments of canonical operators and showed that it is necessary and sufficient for 



1
⊕
1


{\displaystyle 1\oplus 1}

-mode Gaussian states (see Ref. for a seemingly different but essentially equivalent approach). It was later found that Simon's condition is also necessary and sufficient for 



1
⊕
n


{\displaystyle 1\oplus n}

-mode Gaussian states, but no longer sufficient for 



2
⊕
2


{\displaystyle 2\oplus 2}

-mode Gaussian states. Simon's condition can be generalized by taking into account the higher order moments of canonical operators or by using entropic measures.
