Optimal Cloning of Pure States

R. F. Werner

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Optimal Cloning of Pure States

R. F. Werner

Quantum Physics · Submitted 1 Apr 1998

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

The authors' main claim We construct the unique optimal quantum device for turning a finite number of d-level quantum systems in the same unknown pure state \sigma into M systems of the same kind, in an approximation of the M-fold tensor product of the state \sigma.

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What the abstract itself states, as probabilities: claims first 0.08 · states limitation 0.25 · human participants 0.02 · controlled comparison 0.02 · randomized assignment 0.01 · states quantitative result 0.11 · compares with prior results 0.06 · mentions code or data availability 0.02.

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

We construct the unique optimal quantum device for turning a finite number of d-level quantum systems in the same unknown pure state \sigma into M systems of the same kind, in an approximation of the M-fold tensor product of the state \sigma.

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#	sentence	role	the authors' own work	states the main conclusion	strength
s0	We construct the unique optimal quantum device for turning a finite number of d-level quantum systems in the same unknown pure state \sigma into M systems of the same kind, in an approximation of the M-fold tensor product of the state \sigma.	contribution 0.98	0.95	0.86	asserted 1.00

What kind of paper the classifier reports this is: theoretical result 0.65 · evidence from proof or derivation 1.00.

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The paper

Original abstract

We construct the unique optimal quantum device for turning a finite number of d-level quantum systems in the same unknown pure state \sigma into M systems of the same kind, in an approximation of the M-fold tensor product of the state \sigma.

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References

Forward citations

Cited by 4 Pith papers

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

More is Less:Optimal Security for Haar Quantum Money and More
quant-ph 2026-09 accept novelty 7.0 of 10

Forging one extra copy of a Haar-random n-qubit money state from k copies with a reflection oracle requires Theta(2^(n/2)) queries whenever k = o(2^n), independent of k.
A depolarizing choir sings in Gaussian harmony
quant-ph 2026-09 conditional novelty 7.0 of 10

The depolarizing channel acting on symmetric inputs converges to a Gaussian thermal attenuator, and optimized Gaussian codes yield the best-known depolarizing capacity threshold p≥0.2029161.
Sequential quantum processes with group symmetries
quant-ph 2025-10 conditional novelty 7.0 of 10

A canonical streaming circuit decomposition for (G×H)-invariant quantum combs is derived, and numerical optimization suggests a deterministic 7-query transposition protocol for qutrits that is reported as exact.
The Church of the Symmetric Subspace
quant-ph 2013-08 accept novelty 3.0 of 10

A pedagogical review showing that the symmetric subspace unifies optimal cloning, state estimation, the de Finetti theorem, and moment-based concentration of measure in quantum information.

How the literature uses it

9 arXiv papers cite this in 12 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 · 5 sentences without a confident label

Cites it as background 7 papers

The term broadcasting has previously been used in the context of quantum information to signify the extension of the no-cloning theorem [ref] to mixed states [ref] , sometimes phrased in terms of optimal cloning machines [ref] , for a review see [ref] .

Unknown measurement statistics cannot be redundantly copied using finite resources · Broadcasting Versus Semiclassical Broadcasting · 1.00
A quantum cloning process which produces clones that can achieve this bound is referred to as optimal [ref] .

Optimized Telecloning Circuits: Theory and Practice of Nine NISQ Clones · Introduction · 0.95
Examples of such channels are approximate cloning [ref] or broadcasting of quantum information as in Ref. [ref] , although the channel need not be of this form.

Device-independent and semi-device-independent entanglement certification in broadcast Bell scenarios · Bell nonlocality in broadcast scenarios · 0.94

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