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

Kluwer Academic Publishers eBooks

Quantum Tomography, Teleportation, and Cloning

Giacomo Mauro D’Ariano

Published Feb 24, 2006• 0 citations
Publisher

Abstract

In this paper, in a simple unifying matrix framework, I will present general classification of all possible tomography methods, teleportation schemes, and optimal quantum cloning maps. We will see how every tomographic method or teleportation scheme corresponds to a choice of operator spanning sets, and how this framework also leads to methods for engineering new Bell measurements. On the other hand, the classification of all possible covariant cloning maps (that are optimal for a given criterion) includes all known types of cloning, and leads to methods for engineering new cloning machines, which can be physically realized through unitary transformation with ancilla, and/or via probabilistic quantum operations. Fidelity criteria for POVM’s can be exploited to achieve joint POVM’s via cloning. I will give concrete physical realizations in the paper.

DOI
10.1007/0-306-47114-0_13

Related papers

Realization of universal optimal quantum machines by projective operators and stochastic maps

Fabio Sciarrino, Carlo Sias, Marco Ricci +1 more

Optimal quantum machines can be implemented by linear projective operations. In the present work a general qubit symmetrization theory is presented by investigating the close links to the qubit purification process and to the programmable teleportation of any generic optimal antiunitary map. In addition, the contextual realization of the $N\ensuremath{\rightarrow}M$ cloning map and of the teleportation of the $N\ensuremath{\rightarrow}(M\ensuremath{-}N)$ universal-NOT (UNOT) gate is analyzed by a very general angular momentum theory. An extended set of experimental realizations by state symmetrization linear optical procedures is reported. These include the $1\ensuremath{\rightarrow}2$ cloning process, the UNOT gate and the quantum tomographic characterization of the optimal partial transpose map of polarization encoded qubits.

arXiv:quant-ph/0407176•Physical Review A•Nov 1, 2004•35 citations

Optical Quantum Cloning - a Review

Nicolas J. Cerf, Jaromı́r Fiurášek

After a brief introduction to the quantum no-cloning theorem and its link with the linearity and causality of quantum mechanics, the concept of quantum cloning machines is sketched, following, whenever possible, the chronology of the main results. The important classes of quantum cloning machines are reviewed, in particular state-independent and state-dependent cloning machines. The 1-to-2 cloning problem is then studied from a formal point of view, using the isomorphism between completely positive maps and operators, which leads to the so-called double-Bell ansatz. This also yields an efficient numerical approach to quantum cloning, based on semidefinite programming methods. The derivation of the optimal N-to-M universal cloning machine in d dimensions is then detailed, as well as the notion of asymmetric cloning machines. In the second part of this review, the optical implementation of cloning machines is considered. It is shown that the universal cloning of photons can be achieved by parametric amplification of light or by symmetrization via the Hong-Ou-Mandel effect. The various experimental demonstrations of quantum cloning machines are reviewed. The cloning of orthogonally polarized photons is also considered, as well as the asymmetric and phase-covariant cloning of photons. Finally, the extension of quantum cloning to continuous variables is analyzed. The optimal cloning of coherent states of light by phase-insensitive amplification is explained, as well as the experimental realization of continuous-variable quantum cloning with linear optics, measurement, and feed-forward operations.

arXiv:quant-ph/0512172•Dec 21, 2005•12 citations

Quantum Cloning Machines and the Applications

Heng Fan, Yi-Nan Wang, Jing Li +4 more

No-cloning theorem is fundamental for quantum mechanics and for quantum information science that states an unknown quantum state cannot be cloned perfectly. However, we can try to clone a quantum state approximately with the optimal fidelity, or instead, we can try to clone it perfectly with the largest probability. Thus various quantum cloning machines have been designed for different quantum information protocols. Specifically, quantum cloning machines can be designed to analyze the security of quantum key distribution protocols such as BB84 protocol, six-state protocol, B92 protocol and their generalizations. Some well-known quantum cloning machines include universal quantum cloning machine, phase-covariant cloning machine, the asymmetric quantum cloning machine and the probabilistic quantum cloning machine etc. In the past years, much progress has been made in studying quantum cloning machines and their applications and implementations, both theoretically and experimentally. In this review, we will give a complete description of those important developments about quantum cloning and some related topics. On the other hand, this review is self-consistent, and in particular, we try to present some detailed formulations so that further study can be taken based on those results.

•Jan 1, 2013•63 citations

Quantum cloning and teleportation criteria for continuous quantum variables

Frédéric Grosshans, Philippe Grangier

We discuss the criteria presently used for evaluating the efficiency of quantum teleportation schemes for continuous variables. Using an argument based upon the difference between 1-to-2 quantum cloning (quantum duplication) and 1-to-infinity cloning (classical measurement), we show that a fidelity value larger than 2/3 warrants that the teleported state is the best possible remaining copy of the input state. This value has not been reached experimentally so far.

arXiv:quant-ph/0012121•Physical Review A•Jun 12, 2001•213 citations

Teleportation-based quantum state tomography

Gustavo Rigolin

We explicitly show that the quantum teleportation protocol can be employed to completely reconstruct arbitrary two- and three-qubit density matrices. We also extend the present analysis to n-qubit density matrices. The only quantum resources needed to implement the teleportation-based quantum state tomography protocol are the ability to make Bell measurements and the ability to prepare a few different single qubit states to be teleported from Alice to Bob.

quant-pharXiv:2511.18621•APS Open Science•Nov 25, 2025•1 citation

Quantum Tomography: General Theory and New Experiments

Giacomo Mauro D’Ariano

Quantum tomography is a general method for estimating the ensemble average of all operators of an arbitrary quantum system from a set of measurements of a quorum of observables. A procedure for deconvolving instrumental noise is available, which makes the tomographic method feasible in different physical contexts. Recent developments are presented and new experiments are proposed, which are now made possible by the tomographic technique.

Fortschritte der Physik•May 1, 2000•6 citations
In this paper, in a simple unifying matrix framework, I will present general classification of all possible tomography methods, teleportation schemes, and optimal quantum cloning maps. We will see how every tomographic method or teleportation scheme corresponds to a choice of operator spanning sets, and how this framework also leads to methods for engineering new Bell measurements. On the other hand, the classification of all possible covariant cloning maps (that are optimal for a given criterion) includes all known types of cloning, and leads to methods for engineering new cloning machines, which can be physically realized through unitary transformation with ancilla, and/or via probabilistic quantum operations. Fidelity criteria for POVM’s can be exploited to achieve joint POVM’s via cloning. I will give concrete physical realizations in the paper.
Optimal quantum machines can be implemented by linear projective operations. In the present work a general qubit symmetrization theory is presented by investigating the close links to the qubit purification process and to the programmable teleportation of any generic optimal antiunitary map. In addition, the contextual realization of the $N\ensuremath{\rightarrow}M$ cloning map and of the teleportation of the $N\ensuremath{\rightarrow}(M\ensuremath{-}N)$ universal-NOT (UNOT) gate is analyzed by a very general angular momentum theory. An extended set of experimental realizations by state symmetrization linear optical procedures is reported. These include the $1\ensuremath{\rightarrow}2$ cloning process, the UNOT gate and the quantum tomographic characterization of the optimal partial transpose map of polarization encoded qubits.
After a brief introduction to the quantum no-cloning theorem and its link with the linearity and causality of quantum mechanics, the concept of quantum cloning machines is sketched, following, whenever possible, the chronology of the main results. The important classes of quantum cloning machines are reviewed, in particular state-independent and state-dependent cloning machines. The 1-to-2 cloning problem is then studied from a formal point of view, using the isomorphism between completely positive maps and operators, which leads to the so-called double-Bell ansatz. This also yields an efficient numerical approach to quantum cloning, based on semidefinite programming methods. The derivation of the optimal N-to-M universal cloning machine in d dimensions is then detailed, as well as the notion of asymmetric cloning machines. In the second part of this review, the optical implementation of cloning machines is considered. It is shown that the universal cloning of photons can be achieved by parametric amplification of light or by symmetrization via the Hong-Ou-Mandel effect. The various experimental demonstrations of quantum cloning machines are reviewed. The cloning of orthogonally polarized photons is also considered, as well as the asymmetric and phase-covariant cloning of photons. Finally, the extension of quantum cloning to continuous variables is analyzed. The optimal cloning of coherent states of light by phase-insensitive amplification is explained, as well as the experimental realization of continuous-variable quantum cloning with linear optics, measurement, and feed-forward operations.
No-cloning theorem is fundamental for quantum mechanics and for quantum information science that states an unknown quantum state cannot be cloned perfectly. However, we can try to clone a quantum state approximately with the optimal fidelity, or instead, we can try to clone it perfectly with the largest probability. Thus various quantum cloning machines have been designed for different quantum information protocols. Specifically, quantum cloning machines can be designed to analyze the security of quantum key distribution protocols such as BB84 protocol, six-state protocol, B92 protocol and their generalizations. Some well-known quantum cloning machines include universal quantum cloning machine, phase-covariant cloning machine, the asymmetric quantum cloning machine and the probabilistic quantum cloning machine etc. In the past years, much progress has been made in studying quantum cloning machines and their applications and implementations, both theoretically and experimentally. In this review, we will give a complete description of those important developments about quantum cloning and some related topics. On the other hand, this review is self-consistent, and in particular, we try to present some detailed formulations so that further study can be taken based on those results.