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Rank Lower Bounds on Non-Local Quantum Computation

Authors Vahid R. Asadi , Eric Culf, Alex May

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Author Details

Vahid R. Asadi
  • University of Waterloo, Canada
Eric Culf
  • University of Waterloo, Canada
Alex May
  • Perimeter Institute for Theoretical Physics, Waterloo, Canada
  • University of Waterloo, Canada

Funding

  • May, Alex: Supported by the Perimeter Institute for Theoretical Physics. Research at Perimeter Institute is supported in part by the Government of Canada through the Department of Innovation, Science and Economic Development Canada and by the Province of Ontario through the Ministry of Colleges and Universities.

Acknowledgements

We thank Richard Cleve for helpful discussions during the development of this project. Harry Buhrman and François Le Gall suggested a connection between our bounds and non-deterministic rank, and consequently to non-deterministic quantum communication complexity.

Cite As Get BibTex

Vahid R. Asadi, Eric Culf, and Alex May. Rank Lower Bounds on Non-Local Quantum Computation. In 16th Innovations in Theoretical Computer Science Conference (ITCS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 325, pp. 11:1-11:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025) https://doi.org/10.4230/LIPIcs.ITCS.2025.11

Abstract

A non-local quantum computation (NLQC) replaces an interaction between two quantum systems with a single simultaneous round of communication and shared entanglement. We study two classes of NLQC, f-routing and f-BB84, which are of relevance to classical information theoretic cryptography and quantum position-verification. We give the first non-trivial lower bounds on entanglement in both settings, but are restricted to lower bounding protocols with perfect correctness. Within this setting, we give a lower bound on the Schmidt rank of any entangled state that completes these tasks for a given function f(x,y) in terms of the rank of a matrix g(x,y) whose entries are zero when f(x,y) = 0, and strictly positive otherwise. This also leads to a lower bound on the Schmidt rank in terms of the non-deterministic quantum communication complexity of f(x,y). Because of a relationship between f-routing and the conditional disclosure of secrets (CDS) primitive studied in information theoretic cryptography, we obtain a new technique for lower bounding the randomness complexity of CDS.

Subject Classification

ACM Subject Classification
  • Theory of computation → Quantum information theory
Keywords
  • Non-local quantum computation
  • quantum position-verification
  • conditional disclosure of secrets

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