Zero-knowledge convincing protocol on quantum bit is impossible

Pawel Horodecki; Michal Horodecki; Ryszard Horodecki

doi:10.22331/q-2017-12-23-41

Zero-knowledge convincing protocol on quantum bit is impossible

Pawel Horodecki¹, Michal Horodecki², and Ryszard Horodecki¹

¹Faculty of Applied Physics and Mathematics National Quantum Information Centre Gdánsk University of Technology, 80–233 Gdánsk, Poland
²Institute of Theoretical Physics and Astrophysics, National Quantum Information Centre, Faculty of Mathematics, Physics and Informatics University of Gdánsk, 80-308 Gdánsk, Poland

Published:	2017-12-23, volume 1, page 41
Eprint:	arXiv:quant-ph/0010048v3
Doi:	https://doi.org/10.22331/q-2017-12-23-41
Citation:	Quantum 1, 41 (2017).

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Abstract

Consider two parties: Alice and Bob and suppose that Bob is given a qubit system in a quantum state $\phi$, unknown to him. Alice knows $\phi$ and she is supposed to convince Bob that she knows $\phi$ sending some test message. Is it possible for her to convince Bob providing him "zero knowledge" i. e. no information about $\phi$ he has? We prove that there is no "zero knowledge" protocol of that kind. In fact it turns out that basing on Alice message, Bob (or third party - Eve - who can intercept the message) can synthetize a copy of the unknown qubit state $\phi$ with nonzero probability. This "no-go" result puts general constrains on information processing where information about quantum state is involved.

► BibTeX data

@article{Horodecki2017zeroknowledge,
  doi = {10.22331/q-2017-12-23-41},
  url = {https://doi.org/10.22331/q-2017-12-23-41},
  title = {Zero-knowledge convincing protocol on quantum bit is impossible},
  author = {Horodecki, Pawel and Horodecki, Michal and Horodecki, Ryszard},
  journal = {{Quantum}},
  issn = {2521-327X},
  publisher = {{Verein zur F{\"{o}}rderung des Open Access Publizierens in den Quantenwissenschaften}},
  volume = {1},
  pages = {41},
  month = dec,
  year = {2017}
}

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Cited by

[1] Emily Adlam and Adrian Kent, "Knowledge-Concealing Evidencing of Knowledge About a Quantum State", Physical Review Letters 120 5, 050501 (2018).

[2] Lewis Westfall and Avery Leider, Lecture Notes in Networks and Systems 70, 357 (2020) ISBN:978-3-030-12384-0.

The above citations are from Crossref's cited-by service (last updated successfully 2023-05-29 20:17:33) and SAO/NASA ADS (last updated successfully 2023-05-29 20:17:34). The list may be incomplete as not all publishers provide suitable and complete citation data.

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