Localizing and excluding quantum information; or, how to share a quantum secret in spacetime

Patrick Hayden; Alex May

doi:10.22331/q-2019-10-24-196

Localizing and excluding quantum information; or, how to share a quantum secret in spacetime

Patrick Hayden¹ and Alex May²

¹Stanford University
²The University of British Columbia

Published:	2019-10-24, volume 3, page 196
Eprint:	arXiv:1806.04154v4
Doi:	https://doi.org/10.22331/q-2019-10-24-196
Citation:	Quantum 3, 196 (2019).

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Abstract

When can quantum information be localized to each of a collection of spacetime regions, while also excluded from another collection of regions? We answer this question by defining and analyzing the localize-exclude task, in which a quantum system must be localized to a collection of authorized regions while also being excluded from a set of unauthorized regions. This task is a spacetime analogue of quantum secret sharing, with authorized and unauthorized regions replacing authorized and unauthorized sets of parties. Our analysis yields the first quantum secret sharing scheme for arbitrary access structures for which the number of qubits required scales polynomially with the number of authorized sets. We also study a second related task called state-assembly, in which shares of a quantum system are requested at sets of spacetime points. We fully characterize the conditions under which both the localize-exclude and state-assembly tasks can be achieved, and give explicit protocols. Finally, we propose a cryptographic application of these tasks which we call party-independent transfer.

► BibTeX data

@article{Hayden2019localizingexcluding,
  doi = {10.22331/q-2019-10-24-196},
  url = {https://doi.org/10.22331/q-2019-10-24-196},
  title = {Localizing and excluding quantum information; or, how to share a quantum secret in spacetime},
  author = {Hayden, Patrick and May, Alex},
  journal = {{Quantum}},
  issn = {2521-327X},
  publisher = {{Verein zur F{\"{o}}rderung des Open Access Publizierens in den Quantenwissenschaften}},
  volume = {3},
  pages = {196},
  month = oct,
  year = {2019}
}

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Cited by

[1] Alex May, Jonathan Sorce, and Beni Yoshida, "The connected wedge theorem and its consequences", Journal of High Energy Physics 2022 11, 153 (2022).

[2] Kfir Dolev, Alex May, and Kianna Wan, "Distributing bipartite quantum systems under timing constraints", Journal of Physics A: Mathematical and Theoretical 54 14, 145301 (2021).

[3] Alex May, "Holographic quantum tasks with input and output regions", Journal of High Energy Physics 2021 8, 55 (2021).

[4] Alex May, "Bulk private curves require large conditional mutual information", Journal of High Energy Physics 2021 9, 42 (2021).

[5] Alex May, "Quantum tasks in holography", Journal of High Energy Physics 2019 10, 233 (2019).

[6] Damián Pitalúa-García, "One-out-of-m spacetime-constrained oblivious transfer", Physical Review A 100 1, 012302 (2019).

The above citations are from Crossref's cited-by service (last updated successfully 2023-09-21 12:23:16) and SAO/NASA ADS (last updated successfully 2023-09-21 12:23:17). The list may be incomplete as not all publishers provide suitable and complete citation data.

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