Year: 2024
Type: preprint
Abstract: Finding ways to quantify magic is an important problem in quantum information theory. Recently Leone, Oliviero and Hamma introduced a class of magic measures for qubits, the stabilizer entropies of order $α$, to aid in studying nonstabilizer resource theory. This suggests a way to search for those states that are as distinct as possible from the stabilizer states. In this work we explore the problem in any finite dimension $d$ and characterize the states that saturate an upper bound on stabilizer entropies of order $α\geq2$. Particularly, we show that if a Weyl-Heisenberg (WH) covariant Symmetric Informationally Complete (SIC) quantum measurement exists, its states uniquely maximize the stabilizer entropies by saturating the bound. No other states can reach so high. This result is surprising, as the initial motivation for studying SICs was a purely quantum-foundational concern in QBism. Yet our result may have implications for quantum computation at a practical level, as it demonstrates that this notion of maximal magic inherits all the difficulties of the 25-year-old SIC existence problem, along with the deep questions in number theory associated with it.
Source: arXiv (Cornell University)
Authors: Cuffaro, Gianluca, Fuchs, Christopher A.
Institution: University of Massachusetts Boston
Language: English
Subfield: Artificial Intelligence
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4405957675