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We compute the conjugate system of twisted Araki-Woods von Neumann algebras $\mathcal{L}_T(H) $ for a compatible braided crossing symmetric twist $T$ on afinite dimensional Hilbert space $ \mathcal{H} $ with norm $ \|T\| <1$. Thisimplies that those algebras have finite non-microstates free Fisher informationand therefore are always factors of type $\text{III}_\lambda$ ($0<\lambda\leq1$) or $ \text{II}_1 $. Moreover, using the nontracial free monotone transport,we show that $ \mathcal{L}_T(H) $ is isomorphic to the free Araki-Woods algebra$ \mathcal{L}_0(H) $ when $ \|T\|=q $ is small enough.

A Conjugate System for Twisted Araki-Woods von Neumann Algebras of finite dimensional spaces