Quantum Fisher information from randomized measurements

Aniket Rath; Anna Minguzzi; Beno\^it Vermersch; Cyril Branciard

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Quantum Fisher information from randomized measurements

Aniket Rath, Cyril Branciard, Anna Minguzzi, Benoît Vermersch

Quantum Physics · Submitted 27 May 2021

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

The authors' main claim Using randomized measurements we propose a protocol to accurately estimate these lower bounds in state-of-art quantum technological platforms.

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arXiv ID2105.13164 (version 2)

Pith IDFLB726FZ, Pith's permanent record of this paper and its review

CitationAniket Rath, Anna Minguzzi, Beno\^it Vermersch, Cyril Branciard. "Quantum Fisher information from randomized measurements." arXiv:2105.13164 (2021). https://pith.science/paper/FLB726FZ

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What the abstract itself states, as probabilities: claims first 0.03 · states limitation 0.11 · human participants 0.02 · controlled comparison 0.02 · randomized assignment 0.03 · states quantitative result 0.22 · compares with prior results 0.08 · mentions code or data availability 0.02.

The abstract, sentence by sentence

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

The quantum Fisher information (QFI) is a fundamental quantity of interest in many areas from quantum metrology to quantum information theory. It can in particular be used as a witness to establish the degree of multi-particle entanglement in quantum many-body-systems. In this work, we use polynomials of the density matrix to construct monotonically increasing lower bounds that converge to the QFI. Using randomized measurements we propose a protocol to accurately estimate these lower bounds in state-of-art quantum technological platforms. We estimate the number of measurements needed to achieve a given accuracy and confidence level in the bounds, and present two examples of applications of the method in quantum systems made of coupled qubits and collective spins.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#	sentence	role	the authors' own work	states the main conclusion	strength
s0	The quantum Fisher information (QFI) is a fundamental quantity of interest in many areas from quantum metrology to quantum information theory.	background 1.00	0.04	0.02	asserted 1.00
s1	It can in particular be used as a witness to establish the degree of multi-particle entanglement in quantum many-body-systems.	background 1.00	0.05	0.04	hedged possibility 0.54
s2	In this work, we use polynomials of the density matrix to construct monotonically increasing lower bounds that converge to the QFI.	contribution 0.64	0.94	0.43	asserted 1.00
s3	Using randomized measurements we propose a protocol to accurately estimate these lower bounds in state-of-art quantum technological platforms.	method 0.89	0.87	0.21	asserted 0.77
s4	We estimate the number of measurements needed to achieve a given accuracy and confidence level in the bounds, and present two examples of applications of the method in quantum systems made of coupled qubits and collective spins.	contribution 0.81	0.95	0.24	asserted 1.00

What kind of paper the classifier reports this is: method or tool 1.00 · evidence from proof or derivation 0.89.

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arXiv listing abstract v2

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full text
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The paper

Original abstract

The quantum Fisher information (QFI) is a fundamental quantity of interest in many areas from quantum metrology to quantum information theory. It can in particular be used as a witness to establish the degree of multi-particle entanglement in quantum many-body-systems. In this work, we use polynomials of the density matrix to construct monotonically increasing lower bounds that converge to the QFI. Using randomized measurements we propose a protocol to accurately estimate these lower bounds in state-of-art quantum technological platforms. We estimate the number of measurements needed to achieve a given accuracy and confidence level in the bounds, and present two examples of applications of the method in quantum systems made of coupled qubits and collective spins.

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References

Forward citations

Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

Efficient Quantum Algorithm for Mixed-State Quantum Geometry
quant-ph 2026-10 accept novelty 8.0 of 10 partial

A Gauss-Laguerre quadrature framework reduces the symmetric logarithmic derivative inversion to an exponentially convergent finite sum, yielding resource-efficient block encodings of mixed-state quantum geometry.
Quantum Natural Gradient on Quotient Spaces
quant-ph 2026-08 conditional novelty 6.0 of 10

The circuit QFIM factors as F = B*MB into an intrinsic orbit metric and a circuit-to-orbit differential, making the Moore-Penrose update the exact quotient natural gradient precisely when the prescribed redundancy exh...

How later papers used it

58 later papers cite it

Evidence: substantial. 48 of the citing papers share no author with it, and 7 of those carry a confident label from Pith's citation classifier.

Pith read 14 of the 104 citing sentences, choosing only those whose citation markers point at this paper alone, and wrote the paraphrases from them. The summary, the counts, the evidence level, the links and the quotes come from code; the summary counts the papers listed below. A later paper is listed under a label when Pith's citation classifier gives one of its sentences that label at probability 0.8 or more (0.95 for support), Pith's reading finds that the citing paper itself did it, and a second check confirms the paraphrase against the sentence. This section lists uses only. It does not list criticism or disagreement, so their absence here says nothing about how the paper has been received. Papers that share an author with this one are listed apart, under "By the same authors". A quote is the citing authors' own sentence, shown when their paper's licence is CC BY, CC BY-SA or CC0. JSON

2 later papers by other authors are listed below: 1 used its method or tool and 1 compared its own results with it. 1 more paper by the same authors is listed: 1 used its method or tool.

Uses its method or tool 2 of 5 papers with this label · 1 by the same authors

Began with the monotonic sequence F_n introduced in this paper.

Quantum sensing with critical systems: impact of symmetry, imperfections, and decoherence (2026) · 0.95 · paraphrased: the licence does not allow quoting

By the same authors

Estimated the QFI expressed in terms of a converging series of polynomials of order n in the density matrix, as in this paper, for a state prepared on the 33-qubit IBM superconducting device.

Robust estimation of the Quantum Fisher Information on a quantum processor (2023) (same authors) · 0.92 · paraphrased: the licence does not allow quoting

Compares with it 1 of 4 papers with this label

Therefore, in comparison to the most advanced result obtained so far [ref] , our KST opens up the possibility of efficiently estimating the QFI itself without increasing resource demands.

Krylov shadow tomography: Efficient estimation of quantum Fisher information (2025) · Details on the shadow tomography protocol · 1.00

How the literature uses it

10 arXiv papers cite this in 14 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 · 8 sentences without a confident label

Builds on it 1 paper

We extend the randomized measurement toolbox [ref] to infer the SFF and PSFF from statistical correlations of local random operations applied at different times in a single experiment.

Probing many-body quantum chaos with quantum simulators · Synopsis · 0.87

Uses its method or tool 1 paper

Using Eq. [ref], the bound can be efficiently approximated on NISQ hardware: the QFIM can be estimated efficiently on a quantum device using techniques suggested in Ref. [ref] or Ref. [ref] using classical shadows.

Avoiding barren plateaus using classical shadows · Bounding entanglement increase at a single optimization step · 0.97

Compares with it 1 paper

In contrast to the previous works utilizing randomized measurements to infer properties of many-body quantum states [ref] and (out-of-time-ordered) correlation functions of Heisenberg operators [ref] , the present protocol yields, with the SFF and PSFF, genuine properties of the time evolution operator.

Probing many-body quantum chaos with quantum simulators · Synopsis · 0.96

Cites it as background 3 papers

Related randomized measurement protocols exist that construct lower bounds to the quantum Fisher information [ref] , while Krylov shadow tomography [ref] provides an efficient moment-based reconstruction of such quantities, though it requires multicopy snapshots [ref] .

Certified Fidelity Susceptibility from Classical Shadows · Introduction · 0.88
The recent development of randomized measurements provides us with a general toolbox to measure in a state-agnostic way physical quantities associated with entanglement [ref] , scrambling [ref] , topological order [ref] , and in cross-device quantum verification [ref] .

Importance sampling of randomized measurements for probing entanglement · Introduction · 0.84
Initially, randomized measurements have been proposed and experimentally implemented to characterize many-body quantum states [ref] and (out-of-time-ordered) correlation functions of Heisenberg operators [ref] .

Probing many-body quantum chaos with quantum simulators · Randomized measurements of spectral form factors · 0.88

What it cites · 18 sentences without a confident label

Uses the method or tool of 3 papers

In the case of an a priori unknown noise channel, one can use again the formalism of robust shadows to correct our estimates of $F_n$ [ref] .

Robust shadow estimation · Introduction · 0.94
In the case of an a priori unknown noise channel, one can use again the formalism of robust shadows to correct our estimates of $F_n$ [ref] .

Classical Shadows With Noise · Introduction · 0.94
In the case of an a priori unknown noise channel, one can use again the formalism of robust shadows to correct our estimates of $F_n$ [ref] .

Model-free readout-error mitigation for quantum expectation values · Introduction · 0.94

Cites as background 2 papers

This includes in particular approaches based on the positive partial transpose condition [ref] , which can be applied in the multipartite case [ref] , and on statistical correlations of Pauli measurements [ref] .

Statistically significant tests of multiparticle quantum correlations based on randomized measurements · Introduction · 0.83
This includes in particular approaches based on the positive partial transpose condition [ref] , which can be applied in the multipartite case [ref] , and on statistical correlations of Pauli measurements [ref] .

Experimental estimation of the quantum Fisher information from randomized measurements · Introduction · 0.83

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