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arXiv · 2510.00157

The non-stabilizerness cost of quantum state estimation

Gabriele Lo Monaco·Salvatore Lorenzo·Alessandro Ferraro·Mauro Paternostro·G. Massimo Palma·Luca Innocenti
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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 ${2n}/{\log_2 3}$ 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.

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Gabriele Lo Monaco, Salvatore Lorenzo, Alessandro Ferraro, Mauro Paternostro, G. Massimo Palma, Luca Innocenti. 2025-09-30. The non-stabilizerness cost of quantum state estimation. https://arxiv.org/abs/2510.00157

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