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

Chinese Physics B

Economical phase-covariant cloning with multiclones

Wen‐Hai Zhang, Ye Liu

Published Sep 1, 2009• 2 citations
Publisher

Abstract

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.

DOI
10.1088/1674-1056/18/9/015

Related papers

Optimal Phase-Covariant Cloning in 3 Dimensions

Wen‐Hai Zhang, Longbao Yu, Zhuo‐Liang Cao +1 more

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].

Communications in Theoretical Physics•Jun 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

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

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 realization of phase-covariant devices in arbitrary dimensions (Invited)

Francesco Buscemi, Giacomo Mauro D’Ariano, Chiara Macchiavello

We describe a unified framework of phase-covariant multiuser quantum transformations for d-dimensional quantum systems. We derive the optimal phase-covariant cloning and transposition transformations for multiphase states. We show that for some particular relations between the input and output number of copies, they correspond to economical transformations, which can be achieved without the need of auxiliary systems. We prove a relation between the optimal phase-covariant cloning and transposition maps and optimal estimation of multiple phases for equatorial states.

arXiv:quant-ph/0606120•Journal of the Optical Society of America B•Jan 26, 2007•5 citations

Optimal mirror phase-covariant cloning

Karol Bartkiewicz, Adam Miranowicz, Şahin Kaya Özdemir

We propose a quantum cloning machine, which clones a qubit into two clones assuming known modulus of expectation value of Pauli ${\ensuremath{\sigma}}_{z}$ matrix. The process is referred to as the mirror phase-covariant cloning for which the input state is a priori less known than that for the standard phase-covariant cloning. Analytical expressions describing the cloning transformation and fidelity of the clones are found. Extremal equations for the optimal cloning are derived and analytically solved by generalizing a method of Fiur\'a\ifmmode \check{s}\else \v{s}\fi{}ek [Phys. Rev. A 64, 062310 (2001)]. Quantum circuits implementing the optimal cloning transformation and their physical realization in a quantum-dot system are described.

arXiv:0906.0182•Physical Review A•Sep 3, 2009•30 citations
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.
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)].
We describe a unified framework of phase-covariant multiuser quantum transformations for d-dimensional quantum systems. We derive the optimal phase-covariant cloning and transposition transformations for multiphase states. We show that for some particular relations between the input and output number of copies, they correspond to economical transformations, which can be achieved without the need of auxiliary systems. We prove a relation between the optimal phase-covariant cloning and transposition maps and optimal estimation of multiple phases for equatorial states.
We propose a quantum cloning machine, which clones a qubit into two clones assuming known modulus of expectation value of Pauli ${\ensuremath{\sigma}}_{z}$ matrix. The process is referred to as the mirror phase-covariant cloning for which the input state is a priori less known than that for the standard phase-covariant cloning. Analytical expressions describing the cloning transformation and fidelity of the clones are found. Extremal equations for the optimal cloning are derived and analytically solved by generalizing a method of Fiur\'a\ifmmode \check{s}\else \v{s}\fi{}ek [Phys. Rev. A 64, 062310 (2001)]. Quantum circuits implementing the optimal cloning transformation and their physical realization in a quantum-dot system are described.