Columbia University
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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] Nic Ezzell, Elliott M. Ball, Aliza U. Siddiqui, Mark M. Wilde, Andrew T. Sornborger, Patrick J. Coles, and Zoë Holmes, “Quantum Mixed State Compiling”, arXiv:2209.00528.
[2] 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.
[3] Joran van Apeldoorn, Arjan Cornelissen, András Gilyén, and Giacomo Nannicini, “Quantum tomography using state-preparation unitaries”, arXiv:2207.08800.
[4] Srinivasan Arunachalam, Sergey Bravyi, Arkopal Dutt, and Theodore J. Yoder, “Optimal algorithms for learning quantum phase states”, arXiv:2208.07851.
The above citations are from SAO/NASA ADS (last updated successfully 2023-01-04 02:42:15). The list may be incomplete as not all publishers provide suitable and complete citation data.
On Crossref’s cited-by service no data on citing works was found (last attempt 2023-01-04 02:42:14).
This Paper is published in Quantum under the Creative Commons Attribution 4.0 International (CC BY 4.0) license. Copyright remains with the original copyright holders such as the authors or their institutions.
