Quantifying nonstabilizerness through entanglement spectrum flatness

Non-stabilizerness -also colloquially referred to as magic -is a resource for advantage in quantum computing and lies in the access to non-Clifford operations.Developing a comprehensive understanding of how non-stabilizerness can be quantified and how it relates to other quantum resources is crucial for studying and characterizing the origin of quantum complexity.In this work, we establish a direct connection between non-stabilizerness and entanglement spectrum flatness for a pure quantum state.We show that this connection can be exploited to efficiently probe non-stabilizerness even in the presence of noise.Our results reveal a direct connection between non-stabilizerness and entanglement response, and define a clear experimental protocol to probe non-stabilizerness in cold atom and solid-state platforms.