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| Main Authors: | , , , , , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2510.00157 |
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| _version_ | 1866908613951356928 |
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| author | Monaco, Gabriele Lo Lorenzo, Salvatore Ferraro, Alessandro Paternostro, Mauro Palma, G. Massimo Innocenti, Luca |
| author_facet | Monaco, Gabriele Lo Lorenzo, Salvatore Ferraro, Alessandro Paternostro, Mauro Palma, G. Massimo Innocenti, Luca |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_00157 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The non-stabilizerness cost of quantum state estimation Monaco, Gabriele Lo Lorenzo, Salvatore Ferraro, Alessandro Paternostro, Mauro Palma, G. Massimo Innocenti, Luca Quantum Physics 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. |
| title | The non-stabilizerness cost of quantum state estimation |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2510.00157 |