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

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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.

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[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).

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