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:1104.4014 · Physical Review A

Unified universal quantum cloning machine and fidelities

Yi-Nan Wang, Handuo Shi, Zhao-Xi Xiong, Jing Li, Xi-Jun Ren, Liang-Zhu Mu, Heng Fan

Published Sep 14, 2011• 24 citations
arXivHTMLPDF

Abstract

We present a unified universal quantum cloning machine, which combines several different existing universal cloning machines together, including the asymmetric case. In this unified framework, the identical pure states are projected equally into each copy initially constituted by input and one half of the maximally entangled states. We show explicitly that the output states of those universal cloning machines are the same. One importance of this unified cloning machine is that the cloning procession is always the symmetric projection, which reduces dramatically the difficulties for implementation. Also, it is found that this unified cloning machine can be directly modified to the general asymmetric case. Besides the global fidelity and the single-copy fidelity, we also present all possible arbitrary-copy fidelities.

DOI
10.1103/physreva.84.034302

Related papers

Fidelity Measures in Asymmetric Quantum Cloning

Alastair Kay

We study the problem of universal quantum cloning -- taking several identical copies of a pure but unknown quantum state and producing further copies. While it is well known that it is impossible to perfectly reproduce the state, how well the copies can be cloned can be quantified using the fidelity. We examine how individual fidelities can be traded against each other, and how different fidelity measures can be incorporated. The broadly applicable formalism into which we transform the cloning problem is described as a series of quadratic constraints which are amenable to mathematical and computational scrutiny. As such, we reproduce all known results on optimal universal cloning, and push the recent results on asymmetric cloning much further, giving new trade-off relations between fidelities for broad classes of optimal cloning machines. We also provide substantial evidence that motivates why other parameter ranges (number of input copies) have not, and will not, yield to similar analysis.

•Jul 18, 2014•0 citations

Optimal universal quantum cloning: asymmetries and fidelity measures

Alastair Kay

We study the problem of universal quantum cloning – taking several identical copies of a pure but unknown quantum state and producing further copies. While it is well known that it is impossible to perfectly reproduce the state, how well the copies can be cloned can be quantified using the fidelity. We examine how individual fidelities can be traded against each other, and how different fidelity measures can be incorporated. The broadly applicable formalism into which we transform the cloning problem is described as a series of quadratic constraints which are amenable to mathematical and computational scrutiny. As such, we reproduce all known results on optimal universal cloning, and push the recent results on asymmetric cloning much further, giving new trade-off relations between fidelities for broad classes of optimal cloning machines. We also provide substantial evidence that motivates why other parameter ranges (number of input copies) have not, and will not, yield to similar analysis.

arXiv:1407.4951•Quantum Information and Computation•Sep 1, 2016•10 citations

Realization of a general quantum cloning machine via cavity-assisted interaction

Bao‐Long Fang, Tao Wu, Liu Ye

We present a scheme to realize a general quantum cloning machine via cavity-assisted interaction. First, this scheme can prepare entangled states of three remote trapped atoms including the W state and the GHZ state. Based on this approach, the quantum information carried by a photon pulse or a trapped atom can be copied to other two trapped atoms. According to the known information of the initial state, the equipment can provide the optimal symmetric (asymmetric) universal and phase-covariant quantum cloning. Further, via the cavity input-output process, the quantum cloning can be realized with high fidelity, even if the atom is not localized in the Lamb-Dicke regime.

Europhysics Letters (EPL)•Mar 1, 2012•15 citations

Quantum Cloning and Deletion in Quantum Information Theory

Satyabrata Adhikari

Quantum mechanics put restriction on performing some task which we can do classically. One such restriction is that we cannot copy an arbitrary quantum state. This is known as No-cloning theorem. Although quantum mechanics forbid us to construct a perfect cloner, there is no restriction to construct an imperfect cloner. Therefore, we have constructed and studied a special kind of quantum cloning machine named as Hybrid quantum cloning machine which is nothing but a different combination of pre-existing quantum cloning machines. We showed that this hybrid quantum cloning machine sometime gives better quality copy than the pre-existing quantum cloners. Quantum entanglement is a very astonishing property in a multi-partite system and it is a very useful ingredient of quantum information theory. Therefore broadcasting (cloning) of entanglement is a very important subject to study. In this regard we have studied the broadcasting of entanglement using state dependent quantum cloning machine. Further, we have investigated the problem of secretly broadcasting of three-qubit entangled state between two distant partners. Linearity of quantum mechanics put another restriction on deletion of an arbitrary quantum state i.e. an arbitrary quantum state against a copy cannot be perfectly deleted. Like cloning machine one can construct an approximate deletion machine also. Therefore, we have constructed an universal deletion machine in the sense that the fidelity of deletion does not depend on the input state and showed that the fidelity of deletion is 3/4 . Further we showed that the fidelity of deletion depends on the blank state at the output and it can be improved from the value 3/4 for certain blank state. Moreover, we have studied the case where two cloned copies are given at the input of the deletion machine.

arXiv:0902.1622•Feb 10, 2009•2 citations

Realization of the Unified Quantum Cloning Machine Based on cavity QED

Xue Li, Ren Yi-Ming, Nian-Quan Jiang

Based on cavity QED, we first propose the unified scheme to implement the 1→2 optimal universal quantum cloning machine for arbitrary input state, the asymmetric 1→2 phase-covariant cloning and the 1→3 optimal asymmetric economical phase-covariant quantum cloning machine for the equatorial input state. During the cloning process, due to atoms interacting with a highly detuned cavity mode, thus the scheme is insensitive to the cavity decay and thermal field.

•Jan 1, 2017•0 citations

Quantum circuits for asymmetric 1 to n quantum cloning

Xi-Jun Ren, Heng Fan

In this paper, we considered asymmetric $1\rightarrow n$ cloning circuits generalized from the asymmetric $1\rightarrow 2$ cloning circuit proposed by Bu\v{z}ek \textit{et al.} [Phys. Rev. A 56, 3446 (1997)]. The generalization is based on an information flux insight of the original cloning circuit. Specifically, the circuit separately and sequentially transfers the Z-type information and X-type information of the input state to the output copies with controlled-not gates. The initial input state of the clones defines the asymmetry among all output clones. Although the generalized circuits do not perform universally, the averaged fidelities over a uniform distribution of all possible input cloning states saturate the optimal fidelity tradeoff relations of universal asymmetric cloning.

Quantum Information and Computation•Sep 1, 2015•3 citations
We present a unified universal quantum cloning machine, which combines several different existing universal cloning machines together, including the asymmetric case. In this unified framework, the identical pure states are projected equally into each copy initially constituted by input and one half of the maximally entangled states. We show explicitly that the output states of those universal cloning machines are the same. One importance of this unified cloning machine is that the cloning procession is always the symmetric projection, which reduces dramatically the difficulties for implementation. Also, it is found that this unified cloning machine can be directly modified to the general asymmetric case. Besides the global fidelity and the single-copy fidelity, we also present all possible arbitrary-copy fidelities.
We study the problem of universal quantum cloning -- taking several identical copies of a pure but unknown quantum state and producing further copies. While it is well known that it is impossible to perfectly reproduce the state, how well the copies can be cloned can be quantified using the fidelity. We examine how individual fidelities can be traded against each other, and how different fidelity measures can be incorporated. The broadly applicable formalism into which we transform the cloning problem is described as a series of quadratic constraints which are amenable to mathematical and computational scrutiny. As such, we reproduce all known results on optimal universal cloning, and push the recent results on asymmetric cloning much further, giving new trade-off relations between fidelities for broad classes of optimal cloning machines. We also provide substantial evidence that motivates why other parameter ranges (number of input copies) have not, and will not, yield to similar analysis.
We study the problem of universal quantum cloning – taking several identical copies of a pure but unknown quantum state and producing further copies. While it is well known that it is impossible to perfectly reproduce the state, how well the copies can be cloned can be quantified using the fidelity. We examine how individual fidelities can be traded against each other, and how different fidelity measures can be incorporated. The broadly applicable formalism into which we transform the cloning problem is described as a series of quadratic constraints which are amenable to mathematical and computational scrutiny. As such, we reproduce all known results on optimal universal cloning, and push the recent results on asymmetric cloning much further, giving new trade-off relations between fidelities for broad classes of optimal cloning machines. We also provide substantial evidence that motivates why other parameter ranges (number of input copies) have not, and will not, yield to similar analysis.
We present a scheme to realize a general quantum cloning machine via cavity-assisted interaction. First, this scheme can prepare entangled states of three remote trapped atoms including the W state and the GHZ state. Based on this approach, the quantum information carried by a photon pulse or a trapped atom can be copied to other two trapped atoms. According to the known information of the initial state, the equipment can provide the optimal symmetric (asymmetric) universal and phase-covariant quantum cloning. Further, via the cavity input-output process, the quantum cloning can be realized with high fidelity, even if the atom is not localized in the Lamb-Dicke regime.
Quantum mechanics put restriction on performing some task which we can do classically. One such restriction is that we cannot copy an arbitrary quantum state. This is known as No-cloning theorem. Although quantum mechanics forbid us to construct a perfect cloner, there is no restriction to construct an imperfect cloner. Therefore, we have constructed and studied a special kind of quantum cloning machine named as Hybrid quantum cloning machine which is nothing but a different combination of pre-existing quantum cloning machines. We showed that this hybrid quantum cloning machine sometime gives better quality copy than the pre-existing quantum cloners. Quantum entanglement is a very astonishing property in a multi-partite system and it is a very useful ingredient of quantum information theory. Therefore broadcasting (cloning) of entanglement is a very important subject to study. In this regard we have studied the broadcasting of entanglement using state dependent quantum cloning machine. Further, we have investigated the problem of secretly broadcasting of three-qubit entangled state between two distant partners. Linearity of quantum mechanics put another restriction on deletion of an arbitrary quantum state i.e. an arbitrary quantum state against a copy cannot be perfectly deleted. Like cloning machine one can construct an approximate deletion machine also. Therefore, we have constructed an universal deletion machine in the sense that the fidelity of deletion does not depend on the input state and showed that the fidelity of deletion is 3/4 . Further we showed that the fidelity of deletion depends on the blank state at the output and it can be improved from the value 3/4 for certain blank state. Moreover, we have studied the case where two cloned copies are given at the input of the deletion machine.
In this paper, we considered asymmetric 1→n1\rightarrow n1→n cloning circuits generalized from the asymmetric 1→21\rightarrow 21→2 cloning circuit proposed by Bu\v{z}ek \textit{et al.} [Phys. Rev. A 56, 3446 (1997)]. The generalization is based on an information flux insight of the original cloning circuit. Specifically, the circuit separately and sequentially transfers the Z-type information and X-type information of the input state to the output copies with controlled-not gates. The initial input state of the clones defines the asymmetry among all output clones. Although the generalized circuits do not perform universally, the averaged fidelities over a uniform distribution of all possible input cloning states saturate the optimal fidelity tradeoff relations of universal asymmetric cloning.