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

Communications in Theoretical Physics

Optimal Phase-Covariant Cloning in 3 Dimensions

Wen‐Hai Zhang, Longbao Yu, Zhuo‐Liang Cao, Ye Liu

Published Jun 1, 2012• 0 citations
Publisher

Abstract

In this paper, we present the explicit transformations of the optimal 1 → 3, 4, 5 phase-covariant cloning in 3 dimensions. The cloning fidelities are covered by the theoretical bounds of the optimal 1 → 3k, 3k + 1, 3k + 2 phase-covariant cloning of qutrits, where k ≥ 1 is the integral [Phys. Rev. A 67 (2003) 042306].
DOI
10.1088/0253-6102/57/6/09

Related papers

Optimal Phase-Covariant Cloning in 3 Dimensions

张文海, 余龙宝, 曹卓良 +1 more

在这份报纸，我们在场明确的转变最佳 1 3， 4， 5 phase-covariant 在 3 种尺寸克隆。克隆的忠实被理论界限盖住最佳 1 3k， 3k + 1， 3k + qutrits 克隆的 2 phase-covariant，在此 1 是的 k 积分[Phys。加快。一 67 (2003 ) 042306 ] 。

理论物理通讯：英文版•Jan 1, 2012•0 citations

Optimal 1 → M phase-covariant cloning in three dimensions

Wen‐Hai Zhang, Long-Bao Yu, Zhuo‐Liang Cao +1 more

In this paper, we derive the explicit transformations of the optimal 1 → 3, 4, 5 phase-covariant cloning in three dimensions, and then generalize them to the cases of 1 → M = 3n, 3n + 1, 3n + 2 (n ≥ 1 integer) cloning. The clone fidelities are coincident with the theoretical bounds found.

Chinese Physics B•Jul 1, 2014•2 citations

MULTICLONES QUANTUM CLONING OF QUTRITS

Wen‐Hai Zhang, Dai Jie-lin, Zhuo‐Liang Cao +1 more

In this paper, we present the explicit transformations of the optimal 1 → 3 universal quantum and the phase-covariant cloning in 3 dimensions (qutrits). The fidelities of two types of cloners reach the theoretical bounds.

International Journal of Quantum Information•Oct 1, 2010•0 citations

Economical phase-covariant cloning with multiclones

Wen‐Hai Zhang, Ye Liu

This paper presents a very simple method to derive the explicit transformations of the optimal economical 1 to M phase-covariant cloning. The fidelity of clones reaches the theoretic bound [D'Ariano G M and Macchiavello C 2003 Phys. Rev. A 67 042306]. The derived transformations cover the previous contributions [Delgado Y, Lamata L et al. , 2007 Phys. Rev. Lett. 98 150502] in which M must be odd.

Chinese Physics B•Sep 1, 2009•2 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

Optimal real state cloning in d dimensions

Wen‐Hai Zhang, Tao Wu, Liu Ye +1 more

We present an explicit transformation of optimal asymmetric $1\ensuremath{\rightarrow}2$ real state cloning in two dimensions. Interestingly, the distribution of the two fidelities of the cloning is the same as its counterpart in optimal asymmetric phase-covariant cloning. We also generalize the cloner to the $d$-dimensional case and derive the explicit transformation of the optimal symmetric $1\ensuremath{\rightarrow}2$ real state cloning in the $d$-dimensional system. The maximal fidelity of two clones obtained coincides with the theoretical value [P. Vavez and N. J. Cerf, Phys. Rev. A 68, 032313 (2003)].

Physical Review A•Apr 20, 2007•53 citations
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.
We present an explicit transformation of optimal asymmetric $1\ensuremath{\rightarrow}2$ real state cloning in two dimensions. Interestingly, the distribution of the two fidelities of the cloning is the same as its counterpart in optimal asymmetric phase-covariant cloning. We also generalize the cloner to the ddd-dimensional case and derive the explicit transformation of the optimal symmetric $1\ensuremath{\rightarrow}2$ real state cloning in the ddd-dimensional system. The maximal fidelity of two clones obtained coincides with the theoretical value [P. Vavez and N. J. Cerf, Phys. Rev. A 68, 032313 (2003)].