Asymptotic Compression of Interactive Quantum Communication using Type-Constrained de Finetti Reduction

2026-06-23

AI Summary

This work investigates the efficient compression of quantum interactive communication protocols with classical inputs under worst-case input scenarios. To this end, it introduces a novel constrained de Finetti reduction tailored to input types, which transforms worst-case analysis into an independent and identically distributed setting, thereby enabling asymptotic compression. The proposed method establishes an equivalence between prior-free quantum information cost and the amortized quantum communication cost in the worst case, offering a conceptually clean and rigorous proof. This result significantly advances the understanding of the relationship between information and communication costs in quantum communication complexity theory.

Abstract

For many information processing tasks, de Finetti-style theorems can often simplify the analysis in worst-case input scenarios for which the task exhibits some permutation-invariance symmetry, as they can allow for a reduction from an analysis on worst-case inputs to that of i.i.d. inputs. If further information is available on the inputs, it might be advantageous to reflect this information in the de Finetti reduction. In our work, we focus on a form of such constraint, based on the type of the input. This allows us to obtain a conceptually simple proof of a new de Finetti reduction for classical probability distributions, derived from elementary properties from the method of types. We apply our constrained de Finetti reduction to the compression of quantum interactive communication protocols with classical inputs, and prove that the prior-free quantum information cost equals the worst-case input amortized quantum communication cost.

Problem

• de Finetti reduction
• quantum communication
• type constraint
• interactive protocols
• asymptotic compression

Innovation

• type-constrained de Finetti reduction
• quantum interactive communication
• method of types
• quantum information cost
• asymptotic compression