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Generalized Inner Product Estimation with Limited Quantum Communication

Authors Srinivasan Arunachalam , Louis Schatzki

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ACM Subject Classification
  • Theory of computation → Quantum information theory
Keywords
  • Quantum property testing
  • Quantum Distributed Algorithms

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Abstract

In this work, we consider the fundamental task of distributed inner product estimation when allowed limited communication. Suppose Alice and Bob are given k copies of an unknown n-qubit quantum state |ψ⟩,|ϕ⟩ respectively, are allowed to send q qubits to one another, and the task is to estimate |⟨ψ|ϕ⟩|² up to constant additive error. We show that k = Θ(√{2^{n-q}}) copies are essentially necessary and sufficient for this task (extending the work of Anshu, Landau and Liu (STOC'22) who considered the case when q = 0). Additionally, we also consider the task when the goal of the players is to estimate |⟨ψ|M|ϕ⟩|², for arbitrary Hermitian M. For this task we show that certain norms on M determine the sample complexity of estimating |⟨ψ|M|ϕ⟩|² when using only classical communication.

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Srinivasan Arunachalam and Louis Schatzki. Generalized Inner Product Estimation with Limited Quantum Communication. In 42nd International Symposium on Theoretical Aspects of Computer Science (STACS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 327, pp. 11:1-11:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025) https://doi.org/10.4230/LIPIcs.STACS.2025.11

Author Details

Srinivasan Arunachalam
  • IBM Quantum, Almaden, CA, USA
Louis Schatzki
  • Electrical and Computer Engineering, University of Illinois Urbana-Champaign, IL, USA

Funding

We acknowledge support from IBM through the Illinois-IBM Discovery Accelerator Institute.

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