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| Format: | Preprint |
| Publié: |
2023
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| Accès en ligne: | https://arxiv.org/abs/2301.12925 |
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| _version_ | 1866907779977969664 |
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| author | Oufkir, Aadil |
| author_facet | Oufkir, Aadil |
| contents | How many copies of a quantum process are necessary and sufficient to construct an approximate classical description of it? We extend the result of Surawy-Stepney, Kahn, Kueng, and Guta (2022) to show that $\tilde{\mathcal{O}}(d_{\text{in}}^3d_{\text{out}}^3/\varepsilon^2)$ copies are sufficient to learn any quantum channel $C^{d_{\text{in}}\times d_{\text{in}}} \rightarrow C^{d_{\text{out}}\times d_{\text{out}}}$ to within $\varepsilon$ in diamond norm. Moreover, we show that $Ω(d_{\text{in}}^3 d_{\text{out}}^3/\varepsilon^2)$ copies are necessary for any strategy using incoherent non-adaptive measurements. This lower bound applies even for ancilla-assisted strategies. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2301_12925 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Sample-Optimal Quantum Process Tomography with Non-Adaptive Incoherent Measurements Oufkir, Aadil Quantum Physics How many copies of a quantum process are necessary and sufficient to construct an approximate classical description of it? We extend the result of Surawy-Stepney, Kahn, Kueng, and Guta (2022) to show that $\tilde{\mathcal{O}}(d_{\text{in}}^3d_{\text{out}}^3/\varepsilon^2)$ copies are sufficient to learn any quantum channel $C^{d_{\text{in}}\times d_{\text{in}}} \rightarrow C^{d_{\text{out}}\times d_{\text{out}}}$ to within $\varepsilon$ in diamond norm. Moreover, we show that $Ω(d_{\text{in}}^3 d_{\text{out}}^3/\varepsilon^2)$ copies are necessary for any strategy using incoherent non-adaptive measurements. This lower bound applies even for ancilla-assisted strategies. |
| title | Sample-Optimal Quantum Process Tomography with Non-Adaptive Incoherent Measurements |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2301.12925 |