Magic Resources of the Heisenberg Picture

Understand

We study a non-stabilizerness resource theory for operators, which is dual to that describing states.

• We identify that the stabilizer R\'enyi entropy analog in operator space is a good magic monotone satisfying the usual conditions while inheriting efficient computability properties and providing a tight lower bound to the minimum number of non-Clifford gates in a circuit.
• Operationally, this measure quantifies how well an operator can be approximated by one with only a few Pauli strings -- analogous to how entanglement entropy relates to tensor-network truncation.
• A notable advantage of operator stabilizer entropies is their inherent locality, as captured by a Lieb-Robinson bound.