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

Physical Review A

Cloning of qubits with both the cloned state and the state orthogonal to it as inputs

Go Kato

Published Mar 13, 2009• 3 citations
Publisher

Abstract

A universal cloning machine is derived. The machine produces $c$ clones of an unknown qubit from $s$ identical replicas of qubit and $k$ identical replicas of its orthogonal qubit. For the standard cloning machine, i.e., $k=0$, the universal-not machine, $s=0$, and some other cases, the optimum machine is well known. The universal cloning machine derived in this paper gives clones whose fidelity is the same value as that for the optimum machine. In the case of sufficiently large $c$, we show that the clone fidelity generated by the cloning machine from $s\ensuremath{\ne}0$ replicas and $k\ensuremath{\ne}0$ orthogonal replicas is higher than that generated by the optimal cloning machine from $s+k$ replicas in case $s+k\ensuremath{\le}300$.

DOI
10.1103/physreva.79.032315

Related papers

Optimal cloning of qubits from replicas of a qubit and its orthogonal states

Go Kato

We consider the situation where $s$ replicas of a qubit with an unknown state and its orthogonal $k$ replicas are given as an input, and we try to make $c$ clones of the qubit with the unknown state. As a function of $s$, $k$, and $c$, we obtain the optimal fidelity between the qubit with an unknown state and the clone by explicitly giving a completely positive trace-preserving (CPTP) map that represents a cloning machine. We discuss dependency of the fidelity on the values of the parameters $s$, $k$, and $c$.

Physical Review A•Sep 16, 2010•3 citations

Quantum cloning of orthogonal qubits

Jaromı́r Fiurášek, S. Iblisdir, Serge Massar +1 more

Abstract An optimal universal cloning transformation is derived that produces M copies of an unknown qubit from a pair of orthogonal qubits. For M>6, the corresponding cloning fidelity is higher than that of the optimal copying of a pair of identical qubits.

Fortschritte der Physik•Feb 26, 2003•1 citation

Quantum cloning of orthogonal qubits

Jaromı́r Fiurášek, S. Iblisdir, Serge Massar +1 more

An optimal universal cloning transformation is derived that produces M copies of an unknown qubit from a pair of orthogonal qubits. For $M>6,$ the corresponding cloning fidelity is higher than that of the optimal copying of a pair of identical qubits. It is shown that this cloning transformation can be implemented probabilistically via parametric down conversion by feeding the signal and idler modes of a nonlinear crystal with orthogonally polarized photons.

arXiv:quant-ph/0110016•Physical Review A•Apr 5, 2002•37 citations

Universal optimal cloning of qubits and quantum registers

Vladimír Bužek, Mark S. Hillery

We review our recent work on the universal (i.e. input state independent) optimal quantum copying (cloning) of qubits. We present unitary transformations which describe the optimal cloning of a qubit and we present the corresponding quantum logical network. We also present network for an optimal quantum copying ``machine'' (transformation) which produces N+1 identical copies from the original qubit. Here again the quality (fidelity) of the copies does not depend on the state of the original and is only a function of the number of copies, N. In addition, we present the machine which universaly and optimally clones states of quantum objects in arbitrary-dimensional Hilbert spaces. In particular, we discuss universal cloning of quantum registers.

arXiv:quant-ph/9801009•Jan 7, 1998•1 citation

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

Optimal Quantum Cloning Machines

Nicolas Gisin, Serge Massar

We present quantum cloning machines that transform $N$ identical qubits into $M>N$ identical copies and we prove that the fidelity (quality) of these copies is optimal. The connection between cloning and measurement is discussed in detail. When the number of clones $M$ tends towards infinity, the fidelity of each clone tends towards the optimal fidelity that can be obtained by a measurement on the input qubits. More generally, quantum cloning machines are universal devices to translate quantum information into classical information.

arXiv:quant-ph/9705046•Physical Review Letters•Sep 15, 1997•722 citations
A universal cloning machine is derived. The machine produces ccc clones of an unknown qubit from sss identical replicas of qubit and kkk identical replicas of its orthogonal qubit. For the standard cloning machine, i.e., k=0k=0k=0, the universal-not machine, s=0s=0s=0, and some other cases, the optimum machine is well known. The universal cloning machine derived in this paper gives clones whose fidelity is the same value as that for the optimum machine. In the case of sufficiently large ccc, we show that the clone fidelity generated by the cloning machine from s\ensuremath≠0s\ensuremath{\ne}0s\ensuremath=0 replicas and k\ensuremath≠0k\ensuremath{\ne}0k\ensuremath=0 orthogonal replicas is higher than that generated by the optimal cloning machine from s+ks+ks+k replicas in case s+k\ensuremath≤300s+k\ensuremath{\le}300s+k\ensuremath≤300.
We consider the situation where sss replicas of a qubit with an unknown state and its orthogonal kkk replicas are given as an input, and we try to make ccc clones of the qubit with the unknown state. As a function of sss, kkk, and ccc, we obtain the optimal fidelity between the qubit with an unknown state and the clone by explicitly giving a completely positive trace-preserving (CPTP) map that represents a cloning machine. We discuss dependency of the fidelity on the values of the parameters sss, kkk, and ccc.
An optimal universal cloning transformation is derived that produces M copies of an unknown qubit from a pair of orthogonal qubits. For M>6,M>6,M>6, the corresponding cloning fidelity is higher than that of the optimal copying of a pair of identical qubits. It is shown that this cloning transformation can be implemented probabilistically via parametric down conversion by feeding the signal and idler modes of a nonlinear crystal with orthogonally polarized photons.
We review our recent work on the universal (i.e. input state independent) optimal quantum copying (cloning) of qubits. We present unitary transformations which describe the optimal cloning of a qubit and we present the corresponding quantum logical network. We also present network for an optimal quantum copying ``machine'' (transformation) which produces N+1 identical copies from the original qubit. Here again the quality (fidelity) of the copies does not depend on the state of the original and is only a function of the number of copies, N. In addition, we present the machine which universaly and optimally clones states of quantum objects in arbitrary-dimensional Hilbert spaces. In particular, we discuss universal cloning of quantum registers.
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 present quantum cloning machines that transform NNN identical qubits into M>NM>NM>N identical copies and we prove that the fidelity (quality) of these copies is optimal. The connection between cloning and measurement is discussed in detail. When the number of clones MMM tends towards infinity, the fidelity of each clone tends towards the optimal fidelity that can be obtained by a measurement on the input qubits. More generally, quantum cloning machines are universal devices to translate quantum information into classical information.