Speaker
Description
A scrambling unitary never destroys information according to quantum information/Shannon theory. However, this framework alone doesn’t capture the fact that scrambled information can be effectively inaccessible. This limitation points to the need for a new kind of information theory—one that quantifies how much information is scrambled, rather than how much is lost to noise. To address this, we propose introducing a new family of entropies into physics: free entropy. Unlike conventional quantum entropies, which are extensive under tensor independence, free entropy has the defining feature of extensivity under freeness—the appropriate notion of independence pertaining to quantum scrambling.
I will present a preliminary result showing how free entropy naturally arises in a variant of Schumacher compression, providing it with an operational interpretation as the quantum minimum description length of quantum states. I will sketch how this interpretation extends to observables and unitaries, allowing free entropy to capture an operational aspect of quantum scrambling. Finally, I will highlight striking parallels between free entropy and von Neumann entropy, suggesting that free entropy may form the foundation of a new, complementary information theory.
External references
- 25060025
- b1ff7b8c-50d1-4fd5-801f-acce0dbe6b3c
