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

arXiv:quant-ph/0101101 · Physical Review A

Quantum cloning machines for equatorial qubits

Heng Fan, Keiji Matsumoto, Xiang‐Bin Wang, Miki Wadati

Published Dec 10, 2001• 121 citations
arXivHTMLPDF

Abstract

Quantum cloning machines for equatorial qubits are studied. For the case of a one to two phase-covariant quantum cloning machine, we present the networks consisting of quantum gates to realize the quantum cloning transformations. The copied equatorial qubits are shown to be separable by using Peres-Horodecki criterion. The optimal one to M phase-covariant quantum cloning transformations are given.

DOI
10.1103/physreva.65.012304

Related papers

Experimental realization of the optimal universal and phase-covariant quantum cloning machines

Jin‐Shi Xu, Chuan‐Feng Li, Lei Chen +2 more

We experimentally realize the $1\ensuremath{\rightarrow}2$ optimal universal quantum cloning machine for arbitrary qubits and the ancilla-free $1\ensuremath{\rightarrow}3$ optimal phase-covariant quantum cloning machine for $x\text{\ensuremath{-}}y$ equatorial qubits, which were constructed by Zou et al. [Phys. Lett. A 366, 36 (2007)]. The qubits are represented by the polarization states of photons prepared from the process of spontaneous parametric down-conversion. The copies of each machine are shown to have almost equal fidelities conditioned on fourfold coincidences.

Physical Review A•Sep 19, 2008•30 citations

Phase-covariant quantum cloning

Heng Fan, Keiji Matsumoto, Xiang‐Bin Wang +1 more

Quantum cloning machines for equatorial qubits are studied. For a 1 to 2 phase-covariant quantum cloning machine, using Hilbert–Schmidt norm and Bures fidelity, we show that our transformation can achieve the bound of the fidelity.

Journal of Physics A Mathematical and General•Aug 13, 2002•13 citations

Linear optical implementation of ancilla-free 1→3 optimal phase covariant quantum cloning machines for the equatorial qubits

Xu‐Bo Zou, Wolfgang M. Mathis

We propose experimental schemes to implement ancilla-free $1\ensuremath{\rightarrow}3$ optimal phase covariant quantum cloning machines for $x\text{\ensuremath{-}}y$ and $x\text{\ensuremath{-}}z$ equatorial qubits by interfering a polarized photon, which we wish to clone, with different light resources at a six-port symmetric beam splitter. The scheme requires linear optical elements and three-photon coincidence detection, and is feasible with current experimental technology.

Physical Review A•Aug 8, 2005•21 citations

Optimal phase-covariant cloning for qubits and qutrits

Giacomo Mauro D’Ariano, Chiara Macchiavello

We consider cloning transformations of equatorial qubits $|{\ensuremath{\psi}}_{\ensuremath{\varphi}}〉=1/\sqrt{2}(|0〉{+e}^{i\ensuremath{\varphi}}|1〉)$ and qutrits $|{\ensuremath{\psi}}_{\ensuremath{\varphi},\ensuremath{\theta}}〉=1/\sqrt{3}(|0〉{+e}^{i\ensuremath{\varphi}}|1〉{+e}^{i\ensuremath{\theta}}|2〉),$ with the transformation covariant for rotation of the phases $\ensuremath{\varphi}$ and $\ensuremath{\theta}.$ The optimal cloning maps are derived without simplifying assumptions from first principles, for any number of input and output qubits, and for a single-input qutrit and any number of output qutrits. We also compare the cloning maps for global and single-particle fidelities, and we show that the two criteria lead to different optimal maps.

arXiv:quant-ph/0301175•Physical Review A•Apr 11, 2003•104 citations

Generation of phase-covariant quantum cloning

Vahid Karimipour, A. T. Rezakhani

It is known that in phase-covariant quantum cloning, the equatorial states on the Bloch sphere can be cloned with a fidelity higher than the optimal bound established for universal quantum cloning. We generalize this concept to include other states on the Bloch sphere with a definite z component of spin. It is shown that once we know the z component, we can always clone a state with a fidelity higher than the universal value and that of equatorial states. We also make a detailed study of the entanglement properties of the output copies and show that the equatorial states are the only states that give rise to a separable density matrix for the outputs.

arXiv:quant-ph/0208080•Physical Review A•Nov 25, 2002•41 citations

Designing optimal quantum cloning machine for qubit system

Xiaohua Wu, Wu, Fei

Following the work of Niu and Griffiths, in \emph{Phys.Rev.A 58, 4377(1998)}, we shall investigate the problem, how to design the optimal quantum cloning machines (QCMs) for qubit system, with the help of Bloch-sphere representation. In stead of the quality factor there, the Fiuráusek's optimal condition, where the optimal cloning machine should maximize a convex mixture of the average fidelity, is used as the optimality criterion in present protocol. Almost all of the known optimal QCMs in previous works, the cloning for states with fixed polar angle, the phase-covariant cloning, the universal QCMs, the cloning for two arbitrary pure states, and the mirror phase-covariant cloning, should be discussed in a systematic way. The known results, the optimal fidelities for various input ensembles according to different optimality criteria, are recovered here. Our present scheme also offers a general way of constructing the unitary transformation to realize the optimal cloning.

arXiv:1004.5210•Apr 29, 2010•0 citations
Quantum cloning machines for equatorial qubits are studied. For the case of a one to two phase-covariant quantum cloning machine, we present the networks consisting of quantum gates to realize the quantum cloning transformations. The copied equatorial qubits are shown to be separable by using Peres-Horodecki criterion. The optimal one to M phase-covariant quantum cloning transformations are given.
We experimentally realize the $1\ensuremath{\rightarrow}2$ optimal universal quantum cloning machine for arbitrary qubits and the ancilla-free $1\ensuremath{\rightarrow}3$ optimal phase-covariant quantum cloning machine for $x\text{\ensuremath{-}}y$ equatorial qubits, which were constructed by Zou et al. [Phys. Lett. A 366, 36 (2007)]. The qubits are represented by the polarization states of photons prepared from the process of spontaneous parametric down-conversion. The copies of each machine are shown to have almost equal fidelities conditioned on fourfold coincidences.
We propose experimental schemes to implement ancilla-free $1\ensuremath{\rightarrow}3$ optimal phase covariant quantum cloning machines for $x\text{\ensuremath{-}}y$ and $x\text{\ensuremath{-}}z$ equatorial qubits by interfering a polarized photon, which we wish to clone, with different light resources at a six-port symmetric beam splitter. The scheme requires linear optical elements and three-photon coincidence detection, and is feasible with current experimental technology.
We consider cloning transformations of equatorial qubits $|{\ensuremath{\psi}}_{\ensuremath{\varphi}}〉=1/\sqrt{2}(|0〉{+e}^{i\ensuremath{\varphi}}|1〉)$ and qutrits $|{\ensuremath{\psi}}_{\ensuremath{\varphi},\ensuremath{\theta}}〉=1/\sqrt{3}(|0〉{+e}^{i\ensuremath{\varphi}}|1〉{+e}^{i\ensuremath{\theta}}|2〉),$ with the transformation covariant for rotation of the phases $\ensuremath{\varphi}$ and $\ensuremath{\theta}.$ The optimal cloning maps are derived without simplifying assumptions from first principles, for any number of input and output qubits, and for a single-input qutrit and any number of output qutrits. We also compare the cloning maps for global and single-particle fidelities, and we show that the two criteria lead to different optimal maps.
It is known that in phase-covariant quantum cloning, the equatorial states on the Bloch sphere can be cloned with a fidelity higher than the optimal bound established for universal quantum cloning. We generalize this concept to include other states on the Bloch sphere with a definite z component of spin. It is shown that once we know the z component, we can always clone a state with a fidelity higher than the universal value and that of equatorial states. We also make a detailed study of the entanglement properties of the output copies and show that the equatorial states are the only states that give rise to a separable density matrix for the outputs.
Following the work of Niu and Griffiths, in \emph{Phys.Rev.A 58, 4377(1998)}, we shall investigate the problem, how to design the optimal quantum cloning machines (QCMs) for qubit system, with the help of Bloch-sphere representation. In stead of the quality factor there, the Fiuráusek's optimal condition, where the optimal cloning machine should maximize a convex mixture of the average fidelity, is used as the optimality criterion in present protocol. Almost all of the known optimal QCMs in previous works, the cloning for states with fixed polar angle, the phase-covariant cloning, the universal QCMs, the cloning for two arbitrary pure states, and the mirror phase-covariant cloning, should be discussed in a systematic way. The known results, the optimal fidelities for various input ensembles according to different optimality criteria, are recovered here. Our present scheme also offers a general way of constructing the unitary transformation to realize the optimal cloning.