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Quantum Information Processing

Sensitivity of symmetric Boolean functions

  • 01-03-2025
Published in:
Authors
Guoliang Xu
Mengsi Zhang
Binbin Zhang
Tianyin Wang
Yumei Zhang
Published in
Quantum Information Processing | Issue 3/2025

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Abstract

This article explores the sensitivity of symmetric Boolean functions, a crucial aspect of quantum computation and complexity theory. It begins by establishing the significance of Boolean functions in transforming well-known quantum problems and understanding quantum query complexity. The article then delves into the computation of sensitivity for both total and partial symmetric Boolean functions, providing practical methods and theorems that facilitate efficient computation in classical and quantum query models. A key highlight is the investigation into the lower bounds of sensitivity, offering new insights and proving the optimality of certain bounds. The distribution of sensitivity across symmetric Boolean functions is also examined, revealing non-trivial bounds and the prevalence of high sensitivity in these functions. The article concludes by discussing the broader implications of these findings and suggesting avenues for future research, including the generalization of these problems to other complexity measures and Boolean functions.
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previous article Long-distance quantum state transfer via disorder-robust magnons
next article Re-pairing strategy for mode-pairing quantum key distribution
Title
Sensitivity of symmetric Boolean functions
Authors
Guoliang Xu
Mengsi Zhang
Binbin Zhang
Tianyin Wang
Yumei Zhang
Publication date
01-03-2025
Publisher
Springer US
Published in
Quantum Information Processing / Issue 3/2025
Print ISSN: 1570-0755
Electronic ISSN: 1573-1332
DOI
https://doi.org/10.1007/s11128-025-04714-9
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