equivalence of forcing notions

Let $P$ and $Q$ be two forcing notions such that given any generic subset $G$ of $P$ there is a generic subset $H$ of $Q$ with $𝔐[G]=𝔐[H]$ and vice-versa. Then $P$ and $Q$ are equivalent.

Since if $G\in 𝔐[H]$, $\tau [G]\in 𝔐$ for any $P$-name $\tau$, it follows that if $G\in 𝔐[H]$ and $H\in 𝔐[G]$ then $𝔐[G]=𝔐[H]$.