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DOI: 10.4230/LIPIcs.ITCS.2021.11
URN: urn:nbn:de:0030-drops-135504
URL: https://drops.dagstuhl.de/opus/volltexte/2021/13550/
Yu, Nengkun
Sample Efficient Identity Testing and Independence Testing of Quantum States
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Abstract
In this paper, we study the quantum identity testing problem, i.e., testing whether two given quantum states are identical, and quantum independence testing problem, i.e., testing whether a given multipartite quantum state is in tensor product form. For the quantum identity testing problem of 𝒟(ℂ^d) system, we provide a deterministic measurement scheme that uses 𝒪(d²/ε²) copies via independent measurements with d being the dimension of the state and ε being the additive error. For the independence testing problem 𝒟(ℂ^d₁⊗ℂ^{d₂}⊗⋯⊗ℂ^{d_m}) system, we show that the sample complexity is Θ̃((Π_{i = 1}^m d_i)/ε²) via collective measurements, and 𝒪((Π_{i = 1}^m d_i²)/ε²) via independent measurements. If randomized choice of independent measurements are allowed, the sample complexity is Θ(d^{3/2}/ε²) for the quantum identity testing problem, and Θ̃((Π_{i = 1}^m d_i^{3/2})/ε²) for the quantum independence testing problem.
BibTeX - Entry
@InProceedings{yu:LIPIcs.ITCS.2021.11,
author = {Nengkun Yu},
title = {{Sample Efficient Identity Testing and Independence Testing of Quantum States}},
booktitle = {12th Innovations in Theoretical Computer Science Conference (ITCS 2021)},
pages = {11:1--11:20},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-177-1},
ISSN = {1868-8969},
year = {2021},
volume = {185},
editor = {James R. Lee},
publisher = {Schloss Dagstuhl--Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/opus/volltexte/2021/13550},
URN = {urn:nbn:de:0030-drops-135504},
doi = {10.4230/LIPIcs.ITCS.2021.11},
annote = {Keywords: Quantum property testing}
}
| Keywords: | Quantum property testing | |
| Seminar: | 12th Innovations in Theoretical Computer Science Conference (ITCS 2021) | |
| Issue date: | 2021 | |
| Date of publication: | 04.02.2021 |
