Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Quantum Information and Computation

Highly asymmetric quantum cloning in arbitrary dimension

J. Fiuravsek, Radim Filip, Nicolas J. Cerf

Published Nov 1, 2005• 11 citations
Publisher

Abstract

We investigate the universal asymmetric cloning of states in a Hilbert space of arbitrary dimension. We derive the class of optimal and fully asymmetric $1\rightarrow 3$ cloners, which produce three copies, each having a different fidelity. A simple parametric expression for the maximum achievable cloning fidelity triplets is then provided. As a side-product, we also prove the optimality of the $1\rightarrow 2$ asymmetric cloning machines that have been proposed in the literature.

DOI
10.26421/qic5.7-6

Related papers

Highly asymmetric quantum cloning in arbitrary dimension

Jaromı́r Fiurášek, Radim Filip, Nicolas J. Cerf

We investigate the universal asymmetric cloning of states in a Hilbert space of arbitrary dimension. We derive the class of optimal and fully asymmetric 1->3 cloners, which produce three copies, each having a different fidelity. A simple parametric expression for the maximum achievable cloning fidelity triplets is then provided. As a side-product, we also prove the optimality of the 1->2 asymmetric cloning machines that have been proposed in the literature.

arXiv:quant-ph/0505212•Quantum Information and Computation•May 27, 2005•21 citations

Cloning a real d -dimensional quantum state on the edge of the no-signaling condition

Patrick Navez, Nicolas J. Cerf

We investigate the class of quantum cloning machines that equally duplicate all real states in a Hilbert space of arbitrary dimension. By using the no-signaling condition, namely, that cloning cannot make superluminal communication possible, we derive an upper bound on the fidelity of this class of quantum cloning machines. Then, for each dimension d, we construct an optimal symmetric cloner whose fidelity saturates this bound. Similar calculations can also be performed in order to recover the fidelity of the optimal universal cloner in d dimensions.

arXiv:quant-ph/0302172•Physical Review A•Sep 24, 2003•63 citations

Universal Optimal Cloning of Arbitrary Quantum States: From Qubits to Quantum Registers

Vladimír Bužek, Mark S. Hillery

We present the universal cloning transformation of states in arbitrary-dimensional Hilbert spaces. This unitary transformation attains the optimal fidelity of cloning as specified by Werner [Phys. Rev. A 58, 1827 (1998)]. With this cloning transformation, pure as well as impure states can be optimally copied, and the quality of the copies does not depend on the state being copied. We discuss the properties of quantum clones. In particular, we show that in the limit of high dimension the fidelity of clones does not converge to zero but attains the limit $1/2$. We also show that our cloning transformation is most suitable for cloning of entanglement.

Physical Review Letters•Nov 30, 1998•204 citations

Fidelity Measures in Asymmetric Quantum Cloning

Alastair Kay

We study the problem of universal quantum cloning -- taking several identical copies of a pure but unknown quantum state and producing further copies. While it is well known that it is impossible to perfectly reproduce the state, how well the copies can be cloned can be quantified using the fidelity. We examine how individual fidelities can be traded against each other, and how different fidelity measures can be incorporated. The broadly applicable formalism into which we transform the cloning problem is described as a series of quadratic constraints which are amenable to mathematical and computational scrutiny. As such, we reproduce all known results on optimal universal cloning, and push the recent results on asymmetric cloning much further, giving new trade-off relations between fidelities for broad classes of optimal cloning machines. We also provide substantial evidence that motivates why other parameter ranges (number of input copies) have not, and will not, yield to similar analysis.

•Jul 18, 2014•0 citations

Multipartite asymmetric quantum cloning

S. Iblisdir, Antonio Acín, Nicolas J. Cerf +3 more

We investigate the optimal distribution of quantum information over multipartite systems in asymmetric settings. We introduce cloning transformations that take $N$ identical replicas of a pure state in any dimension as input and yield a collection of clones with nonidentical fidelities. As an example, if the clones are partitioned into a set of ${M}_{A}$ clones with fidelity ${F}^{A}$ and another set of ${M}_{B}$ clones with fidelity ${F}^{B}$, the trade-off between these fidelities is analyzed, and particular cases of optimal $N\ensuremath{\rightarrow}{M}_{A}+{M}_{B}$ cloning machines are exhibited. We also present an optimal $1\ensuremath{\rightarrow}1+1+1$ cloning machine, which is an example of a tripartite fully asymmetric cloner. Finally, it is shown how these cloning machines can be optically realized.

arXiv:quant-ph/0411179•Physical Review A•Oct 26, 2005•70 citations

Optimal universal quantum cloning: asymmetries and fidelity measures

Alastair Kay

We study the problem of universal quantum cloning – taking several identical copies of a pure but unknown quantum state and producing further copies. While it is well known that it is impossible to perfectly reproduce the state, how well the copies can be cloned can be quantified using the fidelity. We examine how individual fidelities can be traded against each other, and how different fidelity measures can be incorporated. The broadly applicable formalism into which we transform the cloning problem is described as a series of quadratic constraints which are amenable to mathematical and computational scrutiny. As such, we reproduce all known results on optimal universal cloning, and push the recent results on asymmetric cloning much further, giving new trade-off relations between fidelities for broad classes of optimal cloning machines. We also provide substantial evidence that motivates why other parameter ranges (number of input copies) have not, and will not, yield to similar analysis.

arXiv:1407.4951•Quantum Information and Computation•Sep 1, 2016•10 citations
We investigate the universal asymmetric cloning of states in a Hilbert space of arbitrary dimension. We derive the class of optimal and fully asymmetric 1→31\rightarrow 31→3 cloners, which produce three copies, each having a different fidelity. A simple parametric expression for the maximum achievable cloning fidelity triplets is then provided. As a side-product, we also prove the optimality of the 1→21\rightarrow 21→2 asymmetric cloning machines that have been proposed in the literature.
We investigate the class of quantum cloning machines that equally duplicate all real states in a Hilbert space of arbitrary dimension. By using the no-signaling condition, namely, that cloning cannot make superluminal communication possible, we derive an upper bound on the fidelity of this class of quantum cloning machines. Then, for each dimension d, we construct an optimal symmetric cloner whose fidelity saturates this bound. Similar calculations can also be performed in order to recover the fidelity of the optimal universal cloner in d dimensions.
We present the universal cloning transformation of states in arbitrary-dimensional Hilbert spaces. This unitary transformation attains the optimal fidelity of cloning as specified by Werner [Phys. Rev. A 58, 1827 (1998)]. With this cloning transformation, pure as well as impure states can be optimally copied, and the quality of the copies does not depend on the state being copied. We discuss the properties of quantum clones. In particular, we show that in the limit of high dimension the fidelity of clones does not converge to zero but attains the limit 1/21/21/2. We also show that our cloning transformation is most suitable for cloning of entanglement.
We study the problem of universal quantum cloning -- taking several identical copies of a pure but unknown quantum state and producing further copies. While it is well known that it is impossible to perfectly reproduce the state, how well the copies can be cloned can be quantified using the fidelity. We examine how individual fidelities can be traded against each other, and how different fidelity measures can be incorporated. The broadly applicable formalism into which we transform the cloning problem is described as a series of quadratic constraints which are amenable to mathematical and computational scrutiny. As such, we reproduce all known results on optimal universal cloning, and push the recent results on asymmetric cloning much further, giving new trade-off relations between fidelities for broad classes of optimal cloning machines. We also provide substantial evidence that motivates why other parameter ranges (number of input copies) have not, and will not, yield to similar analysis.
We investigate the optimal distribution of quantum information over multipartite systems in asymmetric settings. We introduce cloning transformations that take NNN identical replicas of a pure state in any dimension as input and yield a collection of clones with nonidentical fidelities. As an example, if the clones are partitioned into a set of MA{M}_{A}MA​ clones with fidelity FA{F}^{A}FA and another set of MB{M}_{B}MB​ clones with fidelity FB{F}^{B}FB, the trade-off between these fidelities is analyzed, and particular cases of optimal $N\ensuremath{\rightarrow}{M}_{A}+{M}_{B}$ cloning machines are exhibited. We also present an optimal $1\ensuremath{\rightarrow}1+1+1$ cloning machine, which is an example of a tripartite fully asymmetric cloner. Finally, it is shown how these cloning machines can be optically realized.
We study the problem of universal quantum cloning – taking several identical copies of a pure but unknown quantum state and producing further copies. While it is well known that it is impossible to perfectly reproduce the state, how well the copies can be cloned can be quantified using the fidelity. We examine how individual fidelities can be traded against each other, and how different fidelity measures can be incorporated. The broadly applicable formalism into which we transform the cloning problem is described as a series of quadratic constraints which are amenable to mathematical and computational scrutiny. As such, we reproduce all known results on optimal universal cloning, and push the recent results on asymmetric cloning much further, giving new trade-off relations between fidelities for broad classes of optimal cloning machines. We also provide substantial evidence that motivates why other parameter ranges (number of input copies) have not, and will not, yield to similar analysis.