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

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.

arXiv comment31 pages, 13 figures. v4 changes license

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Cited by in corpus (4)

• Holographic quantum tasks with input and output regions
• The connected wedge theorem and its consequences
• Bulk private curves require large conditional mutual information
• Distributing bipartite quantum systems under timing constraints