License: Creative Commons Attribution 3.0 Unported license (CC BY 3.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.ITCS.2021.11
URN: urn:nbn:de:0030-drops-135504
URL: https://drops.dagstuhl.de/opus/volltexte/2021/13550/
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Yu, Nengkun

Sample Efficient Identity Testing and Independence Testing of Quantum States

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LIPIcs-ITCS-2021-11.pdf (0.6 MB)


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
Collection: 12th Innovations in Theoretical Computer Science Conference (ITCS 2021)
Issue Date: 2021
Date of publication: 04.02.2021


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