Secret-shared teleportation of a two-qudit gate with a deferred recipient
Abstract
An unknown quantum operation, like an unknown quantum state, cannot be perfectly copied or stored for later use. A specific gate can be embedded in an entangled resource and teleported, but its destination is fixed when the resource is created. Here we show that the capability to apply a two-qudit entangling gate can instead be secret-shared among many parties: the shares are distributed in advance, and a later key release lets exactly one of them, chosen after distribution, exercise it. A provider encrypts half of a Bell pair held with a user into n shares, one per candidate node. The selected node, given the key qudits, completes an exact non-local CSUMk gate with the user's data, in every measurement branch and for any qudit dimension, with the power k chosen by the user alone. Any coalition of fewer than n candidate nodes, or the key register alone, holds no information, unselected nodes cannot tell whether a selection occurred, and the key cannot decrypt twice. For two candidates the registers form a ((3,5)) threshold scheme. Encoder and decoder are explicit O(n) circuits. The construction supports jointly authorized and anonymous gate application, advancing distributed quantum computing and quantum network capabilities.
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BibTeX
@misc{roy2026secretshared,
title = {{Secret-shared teleportation of a two-qudit gate with a deferred recipient}},
author = {Tanay Roy},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.42150},
eprint = {2610.42150},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.42150},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Secret-shared teleportation of a two-qudit gate with a deferred recipient
AU - Tanay Roy
PY - 2026
DA - 2026/10/30
PB - arXiv
DO - 10.48550/arxiv.2610.42150
UR - https://arxiv.org/abs/2610.42150
AB - An unknown quantum operation, like an unknown quantum state, cannot be perfectly copied or stored for later use. A specific gate can be embedded in an entangled resource and teleported, but its destination is fixed when the resource is created. Here we show that the capability to apply a two-qudit entangling gate can instead be secret-shared among many parties: the shares are distributed in advance, and a later key release lets exactly one of them, chosen after distribution, exercise it. A provider encrypts half of a Bell pair held with a user into n shares, one per candidate node. The selected node, given the key qudits, completes an exact non-local CSUM^k gate with the user's data, in every measurement branch and for any qudit dimension, with the power k chosen by the user alone. Any coalition of fewer than n candidate nodes, or the key register alone, holds no information, unselected nodes cannot tell whether a selection occurred, and the key cannot decrypt twice. For two candidates the registers form a ((3,5)) threshold scheme. Encoder and decoder are explicit O(n) circuits. The construction supports jointly authorized and anonymous gate application, advancing distributed quantum computing and quantum network capabilities.
ER -