We present a correspondence between real analytic K\"{a}hler toric manifolds and dually flat spaces, similar to Delzant correspondence in symplectic geometry. This correspondence gives rise to a lifting procedure: if $f:M\to M'$ is an affine isometric map between dually flat spaces and if $N$ and $N'$ are K\"{a}hler toric manifolds associated to $M$ and $M'$, respectively, then there is an equivariant K\"{a}hler immersion $N\to N'$. For example, we show that the Veronese and Segre embeddings are lifts of inclusion maps between appropriate statistical manifolds. We also discuss applications to Quantum Mechanics.

翻译：我们展示了真实分析式K\"{{{{{{{{{{{}}hler toric 元和双平式空间之间的通信,类似于Delzant 通信的共振几何。这种通信产生了一个解除程序:如果$f:M\to M'$是双平式空间之间的等离子等离子图,如果$N和$N'$是K\}{{}a}hler toric entric entros,分别与$和$$有关,那么就有一个等同的K\}{{a}hler 浸泡在$N\\n'$上。例如,我们展示了Veronese和Segre嵌入物是适当的统计式之间的包容性地图的提升。我们还讨论了对量子机械的应用。