Trade-Offs Between Entanglement and Communication

Authors Srinivasan Arunachalam, Uma Girish



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Srinivasan Arunachalam
  • IBM Quantum, Almaden, CA, USA
Uma Girish
  • Princeton University, NJ, USA

Acknowledgements

We thank Vojtech Havlicek and Ran Raz for many discussions during this project. We also thank Ran Raz for feedback on the presentation.

Cite AsGet BibTex

Srinivasan Arunachalam and Uma Girish. Trade-Offs Between Entanglement and Communication. In 38th Computational Complexity Conference (CCC 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 264, pp. 25:1-25:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)
https://doi.org/10.4230/LIPIcs.CCC.2023.25

Abstract

We study the advantages of quantum communication models over classical communication models that are equipped with a limited number of qubits of entanglement. In this direction, we give explicit partial functions on n bits for which reducing the entanglement increases the classical communication complexity exponentially. Our separations are as follows. For every k ≥ ~1: Q‖^* versus R2^*: We show that quantum simultaneous protocols with Θ̃(k⁵log³n) qubits of entanglement can exponentially outperform two-way randomized protocols with O(k) qubits of entanglement. This resolves an open problem from [Dmitry Gavinsky, 2008] and improves the state-of-the-art separations between quantum simultaneous protocols with entanglement and two-way randomized protocols without entanglement [Gavinsky, 2019; Girish et al., 2022]. R‖^* versus Q‖^*: We show that classical simultaneous protocols with Θ̃(k log n) qubits of entanglement can exponentially outperform quantum simultaneous protocols with O(k) qubits of entanglement, resolving an open question from [Gavinsky et al., 2006; Gavinsky, 2019]. The best result prior to our work was a relational separation against protocols without entanglement [Gavinsky et al., 2006]. R‖^* versus R1^*: We show that classical simultaneous protocols with Θ̃(k log n) qubits of entanglement can exponentially outperform randomized one-way protocols with O(k) qubits of entanglement. Prior to our work, only a relational separation was known [Dmitry Gavinsky, 2008].

Subject Classification

ACM Subject Classification
  • Theory of computation → Communication complexity
  • Theory of computation → Quantum communication complexity
Keywords
  • quantum
  • communication complexity
  • exponential separation
  • boolean hidden matching
  • forrelation
  • xor lemma

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