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Estimation of high-dimensional unitary transformations saturating the Quantum Cram\'er-Rao bound

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J. Escandón-Monardes, D. Uzcátegui, M. Rivera-Tapia, S. P. Walborn, A. Delgado

Quantum Physics · Submitted 19 Oct 2023

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

The authors' main claim For $d>2$, the unitary transformations close to the identity are estimated saturating the quantum Cram\'er-Rao bound.

how it is stated · asserted 1.00 read the record →

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arXiv ID2310.12699 (version 2)
Pith ID5WR2FEVU, Pith's permanent record of this paper and its review
CitationA. Delgado, D. Uzc\'ategui, J. Escand\'on-Monardes, M. Rivera-Tapia, S. P. Walborn. "Estimation of high-dimensional unitary transformations saturating the Quantum Cram\'er-Rao bound." arXiv:2310.12699 (2023). https://pith.science/paper/5WR2FEVU
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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.

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Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 3,552 input tokens.

What the abstract itself states, as probabilities: claims first 0.04 · states limitation 0.56 · human participants 0.01 · controlled comparison 0.54 · randomized assignment 0.01 · states quantitative result 0.47 · compares with prior results 0.94 · mentions code or data availability 0.03.

The abstract, sentence by sentence

arXiv listing abstract v2. Results and the main claim are underlined; .

We propose an estimation procedure for $d$-dimensional unitary transformations. For $d>2$, the unitary transformations close to the identity are estimated saturating the quantum Cram\'er-Rao bound. For $d=2$, the estimation of all unitary transformations is also optimal with some prior information. We show through numerical simulations that, even in the absence of prior information, two-dimensional unitary transformations can be estimated with greater precision than by means of standard quantum process tomography.

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 propose an estimation procedure for $d$-dimensional unitary transformations. contribution 0.97 0.90 0.11 asserted 0.98
s1 For $d>2$, the unitary transformations close to the identity are estimated saturating the quantum Cram\'er-Rao bound. result 0.89 0.79 0.42 asserted 1.00
s2 For $d=2$, the estimation of all unitary transformations is also optimal with some prior information. result 0.91 0.77 0.19 asserted 0.96
s3 We show through numerical simulations that, even in the absence of prior information, two-dimensional unitary transformations can be estimated with greater precision than by means of standard quantum process tomography. result 0.99 0.94 0.24 asserted 1.00

What kind of paper the classifier reports this is: method or tool 0.99 · evidence from simulation or computation 0.92.

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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 propose an estimation procedure for $d$-dimensional unitary transformations. For $d>2$, the unitary transformations close to the identity are estimated saturating the quantum Cram\'er-Rao bound. For $d=2$, the estimation of all unitary transformations is also optimal with some prior information. We show through numerical simulations that, even in the absence of prior information, two-dimensional unitary transformations can be estimated with greater precision than by means of standard quantum process tomography.

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