<i>N</i>-Sum Box: An Abstraction for Linear Computation Over Many-to-One Quantum Networks - INSPIRE

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N-Sum Box: An Abstraction for Linear Computation Over Many-to-One Quantum Networks

Feb, 2025

19 pages

Published in:

IEEE Trans.Info.Theor. 71 (2025) 2, 1121-1139

Published: Feb, 2025

DOI:

10.1109/TIT.2024.3514921

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Abstract: (IEEE)

Linear computations over quantum many-to-one communication networks offer opportunities for communication cost improvements through schemes that exploit quantum entanglement among transmitters to achieve superdense coding gains, combined with classical techniques such as interference alignment. The problem becomes much more broadly accessible if suitable abstractions can be found for the underlying quantum functionality via classical black box models. This work formalizes such an abstraction in the form of an “N-sum box”, a black box generalization of a two-sum protocol of Song et al. with recent applications to N-server private information retrieval. The N-sum box has a communication cost of N qudits and classical output of a vector of

N~q

-ary digits linearly dependent (via an

N \times 2N

transfer matrix) on

2N

classical inputs distributed among N transmitters. We characterize which transfer matrices are feasible by our construction, both with and without the possibility of additional locally invertible classical operations at the transmitters and receivers. Furthermore, we provide a sample application to Cross-Subspace Alignment (CSA) schemes to obtain efficient instances of Quantum Private Information Retrieval (QPIR) and Quantum Secure Distributed Batch Matrix Multiplication (QSDBMM). We first describe N-sum boxes based on maximal stabilizers and we then consider non-maximal-stabilizer-based constructions to obtain an instance of Quantum Symmetric Private Information Retrieval.

Encoding
Costs
Receivers
Qubit
Protocols
Quantum entanglement
Codes
Wireless networks
Quantum circuit
Optical transmitters

References(30)

Figures(0)

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