An Improved Sample Complexity Lower Bound for (Fidelity) Quantum State Tomography
Columbia University
Published: | 2023-01-03, volume 7, page 890 |
Eprint: | arXiv:2206.11185v2 |
Doi: | https://doi.org/10.22331/q-2023-01-03-890 |
Citation: | Quantum 7, 890 (2023). |
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Abstract
We show that $\Omega(rd/\epsilon)$ copies of an unknown rank-$r$, dimension-$d$ quantum mixed state are necessary in order to learn a classical description with $1 – \epsilon$ fidelity. This improves upon the tomography lower bounds obtained by Haah, et al. and Wright (when closeness is measured with respect to the fidelity function).
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Cited by
[1] Anurag Anshu and Srinivasan Arunachalam, "A survey on the complexity of learning quantum states", Nature Reviews Physics 6 1, 59 (2023).
[2] Xinbiao Wang, Yuxuan Du, Zhuozhuo Tu, Yong Luo, Xiao Yuan, and Dacheng Tao, "Transition role of entangled data in quantum machine learning", Nature Communications 15 1, 3716 (2024).
[3] Subhadeep Mondal and Amit Kumar Dutta, "A modified least squares-based tomography with density matrix perturbation and linear entropy consideration along with performance analysis", New Journal of Physics 25 8, 083051 (2023).
[4] Rafael Wagner, Zohar Schwartzman-Nowik, Ismael L Paiva, Amit Te’eni, Antonio Ruiz-Molero, Rui Soares Barbosa, Eliahu Cohen, and Ernesto F Galvão, "Quantum circuits for measuring weak values, Kirkwood–Dirac quasiprobability distributions, and state spectra", Quantum Science and Technology 9 1, 015030 (2024).
[5] Ziv Goldfeld, Dhrumil Patel, Sreejith Sreekumar, and Mark M. Wilde, "Quantum neural estimation of entropies", Physical Review A 109 3, 032431 (2024).
[6] Yi Shen and Lin Chen, "Additivity of states uniquely determined by marginals", Physical Review A 108 6, 062418 (2023).
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[8] Nic Ezzell, Elliott M. Ball, Aliza U. Siddiqui, Mark M. Wilde, Andrew T. Sornborger, Patrick J. Coles, and Zoë Holmes, "Quantum mixed state compiling", Quantum Science and Technology 8 3, 035001 (2023).
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[10] Joran van Apeldoorn, Arjan Cornelissen, András Gilyén, and Giacomo Nannicini, "Quantum tomography using state-preparation unitaries", arXiv:2207.08800, (2022).
[11] Ming-Chien Hsu, En-Jui Kuo, Wei-Hsuan Yu, Jian-Feng Cai, and Min-Hsiu Hsieh, "Quantum state tomography via non-convex Riemannian gradient descent", arXiv:2210.04717, (2022).
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