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Quantum testers for hidden group properties

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Katalin Friedl, Frederic Magniez, Miklos Santha, Pranab Sen

Quantum Physics · Submitted 29 Aug 2002

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim We construct efficient or query efficient quantum property testers for two existential group properties which have exponential query complexity both for their decision problem in the quantum and for their testing problem in the classical model of computing.

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arXiv IDquant-ph/0208184 (version 1)
Pith IDAJ3OZGYD, Pith's permanent record of this paper and its review
CitationFrederic Magniez, Katalin Friedl, Miklos Santha, Pranab Sen. "Quantum testers for hidden group properties." arXiv:quant-ph/0208184 (2002). https://pith.science/paper/AJ3OZGYD
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Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 4,220 input tokens.

What the abstract itself states, as probabilities: claims first 0.07 · states limitation 0.42 · human participants 0.01 · controlled comparison 0.04 · randomized assignment 0.03 · states quantitative result 0.24 · compares with prior results 0.86 · mentions code or data availability 0.02.

The abstract, sentence by sentence

arXiv listing abstract v1. Results and the main claim are underlined; .

We construct efficient or query efficient quantum property testers for two existential group properties which have exponential query complexity both for their decision problem in the quantum and for their testing problem in the classical model of computing. These are periodicity in groups and the common coset range property of two functions having identical ranges within each coset of some normal subgroup. Our periodicity tester is efficient in Abelian groups and generalizes, in several aspects, previous periodicity testers. This is achieved by introducing a technique refining the majority correction process widely used for proving robustness of algebraic properties. The periodicity tester in non-Abelian groups and the common coset range tester are query efficient.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#sentencerolethe authors' own workstates the main conclusionstrength
s0 We construct efficient or query efficient quantum property testers for two existential group properties which have exponential query complexity both for their decision problem in the quantum and for their testing problem in the classical model of computing. contribution 0.96 0.95 0.84 asserted 1.00
s1 These are periodicity in groups and the common coset range property of two functions having identical ranges within each coset of some normal subgroup. contribution 0.74 0.44 0.09 asserted 0.97
s2 Our periodicity tester is efficient in Abelian groups and generalizes, in several aspects, previous periodicity testers. result 0.65 0.88 0.15 asserted 1.00
s3 This is achieved by introducing a technique refining the majority correction process widely used for proving robustness of algebraic properties. method 0.97 0.85 0.05 asserted 1.00
s4 The periodicity tester in non-Abelian groups and the common coset range tester are query efficient. result 0.94 0.91 0.29 asserted 1.00

What kind of paper the classifier reports this is: method or tool 0.84 · evidence from proof or derivation 1.00.

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Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

The paper
Original abstract

We construct efficient or query efficient quantum property testers for two existential group properties which have exponential query complexity both for their decision problem in the quantum and for their testing problem in the classical model of computing. These are periodicity in groups and the common coset range property of two functions having identical ranges within each coset of some normal subgroup. Our periodicity tester is efficient in Abelian groups and generalizes, in several aspects, previous periodicity testers. This is achieved by introducing a technique refining the majority correction process widely used for proving robustness of algebraic properties. The periodicity tester in non-Abelian groups and the common coset range tester are query efficient.

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