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:1009.2869 · Physical Review Letters

Experimental Optimal Cloning of Four-Dimensional Quantum States of Photons

Eleonora Nagali, Daniel Giovannini, Lorenzo Marrucci, Sergei Slussarenko, Enrico Santamato, Fabio Sciarrino

Published Aug 13, 2010• 96 citations
arXivHTMLPDF

Abstract

Optimal quantum cloning is the process of making one or more copies of an arbitrary unknown input quantum state with the highest possible fidelity. All reported demonstrations of quantum cloning have so far been limited to copying two-dimensional quantum states, or qubits. We report the experimental realization of the optimal quantum cloning of four-dimensional quantum states, or ququarts, encoded in the polarization and orbital angular momentum degrees of freedom of photons. Our procedure, based on the symmetrization method, is also shown to be generally applicable to quantum states of arbitrarily high dimension-or qudits-and to be scalable to an arbitrary number of copies, in all cases remaining optimal. Furthermore, we report the bosonic coalescence of two single-particle entangled states.

DOI
10.1103/physrevlett.105.073602

Related papers

High-dimensional quantum cloning and applications to quantum hacking

Frédéric Bouchard, Robert Fickler, Robert W. Boyd +1 more

Attempts at cloning a quantum system result in the introduction of imperfections in the state of the copies. This is a consequence of the no-cloning theorem, which is a fundamental law of quantum physics and the backbone of security for quantum communications. Although such perfect copies are prohibited, a quantum state may be copied with maximal accuracy via various optimal cloning schemes. Optimal quantum cloning, which lies at the border of the physical limit imposed by the no-signalling theorem and the Heisenberg uncertainty principle, has been experimentally realized for low dimensional photonic states. However, an increase in the dimensionality of quantum systems is greatly beneficial to quantum computation and communication protocols. Nonetheless, no experimental demonstration of optimal cloning machines has hitherto been shown for high-dimensional quantum systems. Here, we perform optimal cloning of high-dimensional photonic states by means of the symmetrization method. We show the universality of our technique by conducting cloning of numerous arbitrary input states, and fully characterize our cloning machine by performing quantum state tomography on \emph{cloned} photons. In addition, a cloning attack on a Bennett and Brassard (BB84) quantum key distribution protocol is experimentally demonstrated in order to reveal the robustness of high-dimensional states in quantum cryptography.

arXiv:1608.04396•Aug 15, 2016•0 citations

High-dimensional quantum cloning and applications to quantum hacking

Frédéric Bouchard, Robert Fickler, Robert W. Boyd +1 more

Attempts at cloning a quantum system result in the introduction of imperfections in the state of the copies. This is a consequence of the no-cloning theorem, which is a fundamental law of quantum physics and the backbone of security for quantum communications. Although perfect copies are prohibited, a quantum state may be copied with maximal accuracy via various optimal cloning schemes. Optimal quantum cloning, which lies at the border of the physical limit imposed by the no-signaling theorem and the Heisenberg uncertainty principle, has been experimentally realized for low-dimensional photonic states. However, an increase in the dimensionality of quantum systems is greatly beneficial to quantum computation and communication protocols. Nonetheless, no experimental demonstration of optimal cloning machines has hitherto been shown for high-dimensional quantum systems. We perform optimal cloning of high-dimensional photonic states by means of the symmetrization method. We show the universality of our technique by conducting cloning of numerous arbitrary input states and fully characterize our cloning machine by performing quantum state tomography on cloned photons. In addition, a cloning attack on a Bennett and Brassard (BB84) quantum key distribution protocol is experimentally demonstrated to reveal the robustness of high-dimensional states in quantum cryptography.

Science Advances•Feb 3, 2017•138 citations

Experimental demonstration of optimal universal asymmetric quantum cloning of polarization states of single photons by partial symmetrization

Antonín Černoch, Jan Soubusta, Lucie Čelechovská +2 more

We report on experimental implementation of the optimal universal asymmetric $1\ensuremath{\rightarrow}2$ quantum cloning machine for qubits encoded into polarization states of single photons. Our linear-optical machine performs asymmetric cloning by partially symmetrizing the input polarization state of signal photon and a blank copy idler photon prepared in a maximally mixed state. We show that the employed method of measurement of mean clone fidelities exhibits strong resilience to imperfect calibration of the relative efficiencies of single-photon detectors used in the experiment. Reliable characterization of the quantum cloner is thus possible even when precise detector calibration is difficult to achieve.

arXiv:0911.1227•Physical Review A•Dec 2, 2009•6 citations

Optimal copy complexity of quantum state cloning

Sangwoo Jeon, Vaughn Sohn, Changhun Oh

Quantum state cloning is the task of approximately producing additional copies of an unknown quantum state from a finite number of input copies. The optimal cloning fidelity is known exactly for pure states, but no comparable characterization is known for general mixed states. We determine the optimal asymptotic copy complexity for $d$-dimensional states of rank at most $r$: producing $M$ additional copies with worst-case fidelity at least $1-\varepsilon$ requires and is achievable with $N=Θ(Mrd/\varepsilon)$ input copies. Remarkably, the lower bound already holds for a family of states with a fixed flat spectrum, while the matching upper bound is achieved by random purification followed by optimal pure-state cloning. For $M=1$, we further show that high-fidelity tomography can be coherently converted into cloning with comparable error, revealing an operational origin of the matching cloning and tomography complexities.

quant-pharXiv:2608.24484•Aug 26, 2026•0 citations

Clonagem quântica de qudits

Denise F. Ávila

One of the main differences between classical and quantum information is that the former can be replicated. That is, we can easily obtain copies from classical bits but, while dealing with qubits and qudits, we are subject to Quantum Mechanic¿s rules, which determines that arbitrary quantum states cannot be perfectly copied. Still, we can use the so called Quantum Cloning Machines to try and obtain approximate copies with the highest Fidelity or perfect copies with bigger success rates. Those machines are also tools that can be used to study a variety of tasks like, for example, the security analysis of quantum cryptography protocols and quantum state discrimination. One of the aims of this work is to present a brief review of some research about the quantum cloning theory as well as previous discussions on non-cloning theorem, including Herbert¿s proposal for superluminal communication. This work¿s second aim is to analyse an experimental realization and is based on the optical implementation of the so-called optimal universal quan- tum cloning machines for hybrid ququarts encoded in the polarization and orbital angular momentum degrees of freedom of photons, proposed by Na- gali et al.{Phys. Rev. Lett. 105, 073602 }. The implementation is based on the Hong-Ou-Mandel effect and on the photons produced by Parametric Down Conversion. We presented all the concerned theory and obtained the theoretical Fidelity curve predicted by using the quantum state propagation through the optical elements present on the circuit. We also proposed an implementation change for the use of qudits encoded in transversal momen- tum.

•Aug 6, 2015•0 citations

Nonlocal optimal probabilistic cloning of qubit states via twin photons

G. Araneda, Nataly Cisternas, O. Jiménez +1 more

Here we propose a feasible experimental setup for implementing optimal probabilistic cloning of two arbitrary nonorthogonal qubit states. This proposal is based on linear optics together with a pair of entangled twin photons generated via spontaneous parametric down-conversion. The states to be cloned are encoded in the polarization degree of freedom of one of the photons while two perfect clones are generated and encoded in the polarization and the spatial degree of freedom of the resting photon. Therefore, the clones are produced nonlocally. The proposed implementation requires the application of recovery unitary operations onto the photon hosting the clones which are conditional on measurements performed on the other photon in a process akin to quantum teleportation.

Physical Review A•Nov 29, 2012•14 citations
Optimal quantum cloning is the process of making one or more copies of an arbitrary unknown input quantum state with the highest possible fidelity. All reported demonstrations of quantum cloning have so far been limited to copying two-dimensional quantum states, or qubits. We report the experimental realization of the optimal quantum cloning of four-dimensional quantum states, or ququarts, encoded in the polarization and orbital angular momentum degrees of freedom of photons. Our procedure, based on the symmetrization method, is also shown to be generally applicable to quantum states of arbitrarily high dimension-or qudits-and to be scalable to an arbitrary number of copies, in all cases remaining optimal. Furthermore, we report the bosonic coalescence of two single-particle entangled states.
Attempts at cloning a quantum system result in the introduction of imperfections in the state of the copies. This is a consequence of the no-cloning theorem, which is a fundamental law of quantum physics and the backbone of security for quantum communications. Although such perfect copies are prohibited, a quantum state may be copied with maximal accuracy via various optimal cloning schemes. Optimal quantum cloning, which lies at the border of the physical limit imposed by the no-signalling theorem and the Heisenberg uncertainty principle, has been experimentally realized for low dimensional photonic states. However, an increase in the dimensionality of quantum systems is greatly beneficial to quantum computation and communication protocols. Nonetheless, no experimental demonstration of optimal cloning machines has hitherto been shown for high-dimensional quantum systems. Here, we perform optimal cloning of high-dimensional photonic states by means of the symmetrization method. We show the universality of our technique by conducting cloning of numerous arbitrary input states, and fully characterize our cloning machine by performing quantum state tomography on \emph{cloned} photons. In addition, a cloning attack on a Bennett and Brassard (BB84) quantum key distribution protocol is experimentally demonstrated in order to reveal the robustness of high-dimensional states in quantum cryptography.
Attempts at cloning a quantum system result in the introduction of imperfections in the state of the copies. This is a consequence of the no-cloning theorem, which is a fundamental law of quantum physics and the backbone of security for quantum communications. Although perfect copies are prohibited, a quantum state may be copied with maximal accuracy via various optimal cloning schemes. Optimal quantum cloning, which lies at the border of the physical limit imposed by the no-signaling theorem and the Heisenberg uncertainty principle, has been experimentally realized for low-dimensional photonic states. However, an increase in the dimensionality of quantum systems is greatly beneficial to quantum computation and communication protocols. Nonetheless, no experimental demonstration of optimal cloning machines has hitherto been shown for high-dimensional quantum systems. We perform optimal cloning of high-dimensional photonic states by means of the symmetrization method. We show the universality of our technique by conducting cloning of numerous arbitrary input states and fully characterize our cloning machine by performing quantum state tomography on cloned photons. In addition, a cloning attack on a Bennett and Brassard (BB84) quantum key distribution protocol is experimentally demonstrated to reveal the robustness of high-dimensional states in quantum cryptography.
We report on experimental implementation of the optimal universal asymmetric $1\ensuremath{\rightarrow}2$ quantum cloning machine for qubits encoded into polarization states of single photons. Our linear-optical machine performs asymmetric cloning by partially symmetrizing the input polarization state of signal photon and a blank copy idler photon prepared in a maximally mixed state. We show that the employed method of measurement of mean clone fidelities exhibits strong resilience to imperfect calibration of the relative efficiencies of single-photon detectors used in the experiment. Reliable characterization of the quantum cloner is thus possible even when precise detector calibration is difficult to achieve.
Quantum state cloning is the task of approximately producing additional copies of an unknown quantum state from a finite number of input copies. The optimal cloning fidelity is known exactly for pure states, but no comparable characterization is known for general mixed states. We determine the optimal asymptotic copy complexity for ddd-dimensional states of rank at most rrr: producing MMM additional copies with worst-case fidelity at least 1−ε1-\varepsilon1−ε requires and is achievable with N=Θ(Mrd/ε)N=Θ(Mrd/\varepsilon)N=Θ(Mrd/ε) input copies. Remarkably, the lower bound already holds for a family of states with a fixed flat spectrum, while the matching upper bound is achieved by random purification followed by optimal pure-state cloning. For M=1M=1M=1, we further show that high-fidelity tomography can be coherently converted into cloning with comparable error, revealing an operational origin of the matching cloning and tomography complexities.
One of the main differences between classical and quantum information is that the former can be replicated. That is, we can easily obtain copies from classical bits but, while dealing with qubits and qudits, we are subject to Quantum Mechanic¿s rules, which determines that arbitrary quantum states cannot be perfectly copied. Still, we can use the so called Quantum Cloning Machines to try and obtain approximate copies with the highest Fidelity or perfect copies with bigger success rates. Those machines are also tools that can be used to study a variety of tasks like, for example, the security analysis of quantum cryptography protocols and quantum state discrimination. One of the aims of this work is to present a brief review of some research about the quantum cloning theory as well as previous discussions on non-cloning theorem, including Herbert¿s proposal for superluminal communication. This work¿s second aim is to analyse an experimental realization and is based on the optical implementation of the so-called optimal universal quan- tum cloning machines for hybrid ququarts encoded in the polarization and orbital angular momentum degrees of freedom of photons, proposed by Na- gali et al.{Phys. Rev. Lett. 105, 073602 }. The implementation is based on the Hong-Ou-Mandel effect and on the photons produced by Parametric Down Conversion. We presented all the concerned theory and obtained the theoretical Fidelity curve predicted by using the quantum state propagation through the optical elements present on the circuit. We also proposed an implementation change for the use of qudits encoded in transversal momen- tum.
Here we propose a feasible experimental setup for implementing optimal probabilistic cloning of two arbitrary nonorthogonal qubit states. This proposal is based on linear optics together with a pair of entangled twin photons generated via spontaneous parametric down-conversion. The states to be cloned are encoded in the polarization degree of freedom of one of the photons while two perfect clones are generated and encoded in the polarization and the spatial degree of freedom of the resting photon. Therefore, the clones are produced nonlocally. The proposed implementation requires the application of recovery unitary operations onto the photon hosting the clones which are conditional on measurements performed on the other photon in a process akin to quantum teleportation.