In free probability theory, free entropy was introduced by Voiculescu as a technical tool to study free group algebras. It generalizes Shannon entropy to non-commutative random variables based on the idea of non-commutative distributions. This is fundamentally distinct from another more well-known von Neumann entropy, which generalizes Shannon entropy based on non-commutative densities. While the latter is central to quantum information science, the physical significance of free entropy remains unexplored. 

In this work, I bring free entropy to physics by giving it an operational meaning. I’ll demonstrate how free entropy naturally emerges in a variant of Schumacher compression, giving it an operational interpretation as the quantum minimum description length of quantum states. This perspective also highlights and illustrates fundamental properties of free additivity, subadditivity, and strong subadditivity of free entropy, drawing intriguing parallels with von Neumann entropy. I will conclude by motivating how free entropy may offer a promising new direction for quantum information and quantum physics.