Abstract
We study the non-stabilizer resources required to achieve informational completeness in single-setting quantum state estimation scenarios. We consider fixed-basis projective measurements preceded by quantum circuits acting on n-qubit input states, allowing ancillary qubits to increase retrievable information. We prove that when only stabilizer resources are allowed, these strategies are always informationally equivalent to projective measurements in a stabilizer basis, and therefore never informationally complete, regardless of the number of ancillas. We then show that incorporating T gates enlarges the accessible information. Specifically, we prove that at least 2n/log23 such gates are necessary for informational completeness, and that 2n suffice. We conjecture that 2n gates are indeed both necessary and sufficient. Finally, we unveil a tight connection between entanglement structure and informational power of measurements implemented with t-doped Clifford circuits. Our results recast notions of "magic" and stabilizerness - typically framed in computational terms - into the setting of quantum metrology.
Gabriele Lo Monaco
Assistant Professor
Salvatore Lorenzo
Associate professor
Luca Innocenti
Assistant Professor
Mauro Paternostro
Full Professor
