Defining quantum divergences via convex optimization

Understand

We introduce a new quantum R\'enyi divergence $D^{\#}_{\alpha}$ for $\alpha \in (1,\infty)$ defined in terms of a convex optimization program.

• This divergence has several desirable computational and operational properties such as an efficient semidefinite programming representation for states and channels, and a chain rule property.
• An important property of this new divergence is that its regularization is equal to the sandwiched (also known as the minimal) quantum R\'enyi divergence.
• This allows us to prove several results.