Stabilizer Rényi entropy*

Although quantum entanglement is a paradigmatic feature of quantum states, it is well known that stabilizer states, possessing volume law of entanglement, can be efficiently simulated on a classical computer. Thus, to unlock the exponential quantum advantage, non-stabilizer states (also dubbed as magic states) constitute an essential ingredient for quantum computation. I will introduce a resource theoretic measure of magic in quantum states called Stabilizer Rényi entropy. Being easily manageable and computable, it is shown to possess a tight connection with Out of Time Order Correlation functions (OTOCs), displaying an intriguing relation between the resource theory of magic and quantum chaos.