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 Cloning Optimal for Joint Measurements

Giacomo Mauro D’Ariano, Massimiliano Federico Sacchi

Published Feb 24, 2006• 2 citations
Publisher

Abstract

We show that universally covariant cloning is not optimal for achieving joint measurements of noncommuting observables with minimum added noise. For such a purpose a cloning transformation that is covariant with respect to a restricted transformation group is needed. These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

DOI
10.1007/0-306-47114-0_26

Related papers

Quantum cloning optimal for joint measurements

Giacomo Mauro D’Ariano, Massimiliano Federico Sacchi

We show that universally covariant cloning is not optimal for achieving joint measurements of noncommuting observables with minimum added noise. For such a purpose a cloning transformation that is covariant with respect to a restricted transformation group is needed.

arXiv:quant-ph/0009080•Sep 20, 2000•0 citations

Joint measurements via quantum cloning

Giacomo Mauro D’Ariano, Chiara Macchiavello, Massimiliano Federico Sacchi

We explore the possibility of achieving the optimal joint measurement of noncommuting observables on a single quantum system by performing conventional measurements of commuting self-adjoint operators on the clones of the original quantum system. We consider the case of both finite- and infinite-dimensional Hilbert spaces. In the former we study the joint measurement of three orthogonal components of a spin ½; in the latter we consider the case of the joint measurement of any pair of noncommuting quadratures of one mode of the electromagnetic field. We show that universal covariant cloning is not ideal for joint measurements, and a suitable nonuniversal covariant cloning is needed.

arXiv:quant-ph/0007062•Journal of Optics B Quantum and Semiclassical Optics•Mar 16, 2001•29 citations

Approximate joint measurements of qubit observables

Paul Busch, Teiko Heinosaari

Joint measurements of qubit observables have recently been studied in conjunction with quantum information processing tasks such as cloning. Considerations of such joint measurements have until now been restricted to a certain class of observables that can be characterized by a form of covariance. Here we investigate conditions for the joint measurability of arbitrary pairs of qubit observables. For pairs of noncommuting sharp qubit observables, a notion of approximate joint measurement is introduced. Optimal approximate joint measurements are shown to lie in the class of covariant joint measurements. The marginal observables found to be optimal approximators are generally not among the coarse-grainings of the observables to be approximated. This yields scope for the improvement of existing joint measurement schemes. Both the quality of the approximations and the intrinsic unsharpness of the approximators are shown to be subject to Heisenberg-type uncertainty relations.

arXiv:0706.1415•Quantum Information and Computation•Sep 1, 2008•51 citations

Joint Measurements on Qubits and Cloning of Observables

Alessandro Ferraro, Matteo G. A. Paris

Cloning of observables, unlike standard cloning of states, aims at copying the information encoded in the statistics of a class of observables rather then on quantum states themselves. In such a process the emphasis is on the quantum operation (evolution plus measurement) necessary to retrieve the original information. We analyze, for qubit systems, the cloning of a class generated by two noncommuting observables, elucidating the relationship between such a process and joint measurements. This helps in establishing an optimality criterion for cloning of observables. We see that, even if the cloning machine is designed to act on the whole class generated by two noncommuting observables, the same optimal performances of a joint measurement can be attained. Finally, the connection with state dependent cloning is enlightened.

arXiv:quant-ph/0701089•Open Systems & Information Dynamics•Jun 1, 2007•9 citations

A Covariant Quantum Stochastic Dilation Theory

Partha Sarathi Chakraborty, Debashish Goswami, Kalyan B. Sinha

A covariant version of the dilation theory for quantum dynamical semigrops is established, including both Bhat-Parthasarathy type and Evans-Hudson type dilation. It is shown in particular that every uniformly continuous quantum dynamical semigroup on a separable C*-algebra or a von Neumann algebra, which is covariant under a suitable group-action, admits a covariant Evans-Hudson dilation in some appropriate Fock space. These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Birkhäuser Boston eBooks•Jan 1, 2001•6 citations

Decoherence and Quantum Error Correction in Frequency Standards

Chiara Macchiavello, Susana F. Huelga, J. I. Cirac +2 more

The precision of frequency measurements performed on trapped ions in the presence of decoherence is analysed. In particular, standard Ramsey spectroscopy on uucorrelated ions and optimal measurements on maximally entangled states are proved to lead to the same resolution, while the best precision is achieved using partially entangled preparations. The use of symrnetrisation procedures is proposed and it is shown how this allows to overcome even the optimal precision achievable when both the initial preparation and the final measurement are optimized. These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Kluwer Academic Publishers eBooks•Dec 19, 2005•11 citations
We show that universally covariant cloning is not optimal for achieving joint measurements of noncommuting observables with minimum added noise. For such a purpose a cloning transformation that is covariant with respect to a restricted transformation group is needed. These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
We explore the possibility of achieving the optimal joint measurement of noncommuting observables on a single quantum system by performing conventional measurements of commuting self-adjoint operators on the clones of the original quantum system. We consider the case of both finite- and infinite-dimensional Hilbert spaces. In the former we study the joint measurement of three orthogonal components of a spin ½; in the latter we consider the case of the joint measurement of any pair of noncommuting quadratures of one mode of the electromagnetic field. We show that universal covariant cloning is not ideal for joint measurements, and a suitable nonuniversal covariant cloning is needed.
Joint measurements of qubit observables have recently been studied in conjunction with quantum information processing tasks such as cloning. Considerations of such joint measurements have until now been restricted to a certain class of observables that can be characterized by a form of covariance. Here we investigate conditions for the joint measurability of arbitrary pairs of qubit observables. For pairs of noncommuting sharp qubit observables, a notion of approximate joint measurement is introduced. Optimal approximate joint measurements are shown to lie in the class of covariant joint measurements. The marginal observables found to be optimal approximators are generally not among the coarse-grainings of the observables to be approximated. This yields scope for the improvement of existing joint measurement schemes. Both the quality of the approximations and the intrinsic unsharpness of the approximators are shown to be subject to Heisenberg-type uncertainty relations.
Cloning of observables, unlike standard cloning of states, aims at copying the information encoded in the statistics of a class of observables rather then on quantum states themselves. In such a process the emphasis is on the quantum operation (evolution plus measurement) necessary to retrieve the original information. We analyze, for qubit systems, the cloning of a class generated by two noncommuting observables, elucidating the relationship between such a process and joint measurements. This helps in establishing an optimality criterion for cloning of observables. We see that, even if the cloning machine is designed to act on the whole class generated by two noncommuting observables, the same optimal performances of a joint measurement can be attained. Finally, the connection with state dependent cloning is enlightened.
A covariant version of the dilation theory for quantum dynamical semigrops is established, including both Bhat-Parthasarathy type and Evans-Hudson type dilation. It is shown in particular that every uniformly continuous quantum dynamical semigroup on a separable C*-algebra or a von Neumann algebra, which is covariant under a suitable group-action, admits a covariant Evans-Hudson dilation in some appropriate Fock space. These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
The precision of frequency measurements performed on trapped ions in the presence of decoherence is analysed. In particular, standard Ramsey spectroscopy on uucorrelated ions and optimal measurements on maximally entangled states are proved to lead to the same resolution, while the best precision is achieved using partially entangled preparations. The use of symrnetrisation procedures is proposed and it is shown how this allows to overcome even the optimal precision achievable when both the initial preparation and the final measurement are optimized. These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.