Pith. Sign in

RECORD

The limitations of nice mutually unbiased bases

PaperPDF from arXiv

data files

Paper breakdownThe authors' claims, conditions and measurements, as JSON Signed receiptProof this review has not been altered
X Bluesky LinkedIn Reddit Hacker News
Michael Aschbacher, Andrew M. Childs, Pawel Wocjan

Quantum Physics · Submitted 8 Dec 2004

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

The authors' main claim We show that the number of resulting mutually unbiased bases can be at most one plus the smallest prime power contained in the dimension, and therefore that this construction cannot improve upon previous approaches.

how it is stated · asserted 0.99 read the record →

Comment (0) Read on arXiv ↗
Cite ▾
arXiv IDquant-ph/0412066 (version 1)
Pith IDGMFP3ZMY, Pith's permanent record of this paper and its review
CitationAndrew M. Childs, Michael Aschbacher, Pawel Wocjan. "The limitations of nice mutually unbiased bases." arXiv:quant-ph/0412066 (2004). https://pith.science/paper/GMFP3ZMY
Claim paper

The compiled record

The paper's own sentences, arranged. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.

Open the compiled record

Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 4,189 input tokens.

What the abstract itself states, as probabilities: claims first 0.04 · states limitation 0.78 · human participants 0.01 · controlled comparison 0.07 · randomized assignment 0.01 · states quantitative result 0.98 · compares with prior results 0.95 · mentions code or data availability 0.02.

The abstract, sentence by sentence

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

Mutually unbiased bases of a Hilbert space can be constructed by partitioning a unitary error basis. We consider this construction when the unitary error basis is a nice error basis. We show that the number of resulting mutually unbiased bases can be at most one plus the smallest prime power contained in the dimension, and therefore that this construction cannot improve upon previous approaches. We prove this by establishing a correspondence between nice mutually unbiased bases and abelian subgroups of the index group of a nice error basis and then bounding the number of such subgroups. This bound also has implications for the construction of certain combinatorial objects called nets.

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 Mutually unbiased bases of a Hilbert space can be constructed by partitioning a unitary error basis. background 1.00 0.07 0.02 asserted 0.90
s1 We consider this construction when the unitary error basis is a nice error basis. contribution 0.59 0.44 0.02 asserted 0.68
s2 We show that the number of resulting mutually unbiased bases can be at most one plus the smallest prime power contained in the dimension, and therefore that this construction cannot improve upon previous approaches. result 0.96 0.94 0.94 asserted 0.99
s3 We prove this by establishing a correspondence between nice mutually unbiased bases and abelian subgroups of the index group of a nice error basis and then bounding the number of such subgroups. method 0.98 0.95 0.09 asserted 1.00
s4 This bound also has implications for the construction of certain combinatorial objects called nets. interpretation 0.99 0.67 0.03 asserted 0.92

What kind of paper the classifier reports this is: theoretical result 1.00 · evidence from proof or derivation 1.00.

What was examined, and what was not

sources read
  • arXiv listing abstract v1
not examined
  • full text
  • figures and tables
  • references and citing sentences
  • relations to other papers
levels run
  • P abstract
not run
  • S sections
  • T body sentences
  • C citations
  • R cross-paper relations

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

Mutually unbiased bases of a Hilbert space can be constructed by partitioning a unitary error basis. We consider this construction when the unitary error basis is a nice error basis. We show that the number of resulting mutually unbiased bases can be at most one plus the smallest prime power contained in the dimension, and therefore that this construction cannot improve upon previous approaches. We prove this by establishing a correspondence between nice mutually unbiased bases and abelian subgroups of the index group of a nice error basis and then bounding the number of such subgroups. This bound also has implications for the construction of certain combinatorial objects called nets.

Human review

How Pith checks papers → · Full audit of this paper →

How the literature uses it

1 arXiv paper cite this in 2 sentences

Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

Papers citing it

Cites it as background 1 paper

Discussion

Know something about this paper? Leave a comment, or highlight any passage above to comment on it.