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International Journal of Quantum Information

EXPERIMENTAL REALIZATIONS OF THE 1 → M UNIVERSAL CLONING MACHINE

L. Masullo, Marco Ricci, Fabio Sciarrino, Veronica Secondi, F. De Martini

Published Jun 1, 2006• 0 citations
Publisher

Abstract

We report the first experimental realizations of the 1 → M universal cloning machine. Two approaches are carefully described: the adoption of a state symmetrization linear optical procedure and of the quantum injected optical parametric amplifier. Furthermore, this device is adopted to generate optimally distinguishable multi-photon quantum superposition states.

DOI
10.1142/s0219749906001943

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We report the first experimental realizations of the 1 → M universal cloning machine. Two approaches are carefully described: the adoption of a state symmetrization linear optical procedure and of the quantum injected optical parametric amplifier. Furthermore, this device is adopted to generate optimally distinguishable multi-photon quantum superposition states.
The new process of quantum-injection into an optical parametric amplifier operating in entangled configuration is adopted to amplify into a large dimensionality spin-½ Hilbert space the quantum entanglement and superposition properties of the photon-couples generated by parametric down-conversion. The invariance properties of the OPA interaction hamiltonian show that, under certain conditions, the device may act as a Universal Quantum Cloning Machine (UQCM) of the input qubits. Preliminary results here reported show the first experimental realization of such a device. The structure of the Wigner function and of the field's correlation functions shows a multiphoton Schrödinger-cat behaviour of the emitted field which is largely detectable against the squeezed-vacuum noise.
Beyond the no-cloning theorem, the universal symmetric quantum cloning machine was first addressed by Bu\ifmmode \check{z}\else \v{z}\fi{}ek and Hillery. Here, we realized the $\stackrel{\ensuremath{\rightarrow}}{1}$2 qubit Bu\ifmmode \check{z}\else \v{z}\fi{}ek-Hillery cloning machine with linear optical devices. This method relies on the representation of several qubits by a single photon. We showed that the fidelities between the two output qubits and the original qubit are both 56\frac{5}{6}65​ (which proved to be the optimal fidelity of $\stackrel{\ensuremath{\rightarrow}}{1}$2 qubit universal cloner) for arbitrary input pure states.
After a brief introduction to the quantum no-cloning theorem and its link with the linearity and causality of quantum mechanics, the concept of quantum cloning machines is sketched, following, whenever possible, the chronology of the main results. The important classes of quantum cloning machines are reviewed, in particular state-independent and state-dependent cloning machines. The 1-to-2 cloning problem is then studied from a formal point of view, using the isomorphism between completely positive maps and operators, which leads to the so-called double-Bell ansatz. This also yields an efficient numerical approach to quantum cloning, based on semidefinite programming methods. The derivation of the optimal N-to-M universal cloning machine in d dimensions is then detailed, as well as the notion of asymmetric cloning machines. In the second part of this review, the optical implementation of cloning machines is considered. It is shown that the universal cloning of photons can be achieved by parametric amplification of light or by symmetrization via the Hong-Ou-Mandel effect. The various experimental demonstrations of quantum cloning machines are reviewed. The cloning of orthogonally polarized photons is also considered, as well as the asymmetric and phase-covariant cloning of photons. Finally, the extension of quantum cloning to continuous variables is analyzed. The optimal cloning of coherent states of light by phase-insensitive amplification is explained, as well as the experimental realization of continuous-variable quantum cloning with linear optics, measurement, and feed-forward operations.
A simultaneous, contextual experimental demonstration of the two processes of cloning an input qubit $|\ensuremath{\Psi}〉$ and of flipping it into the orthogonal qubit $|{\ensuremath{\Psi}}^{\ensuremath{\perp}}〉$ is reported. The adopted experimental apparatus, a quantum-injected optical parametric amplifier is transformed simultaneously into a universal optimal quantum cloning machine and into a universal-NOT quantum-information gate. The two processes, indeed forbidden in their exact form for fundamental quantum limitations, were found to be universal and optimal, i.e., the measured fidelity of both processes F<1F<1F<1 was found close to the limit values evaluated by quantum theory. A contextual theoretical and experimental investigation of these processes, which may represent the basic difference between the classical and the quantum worlds, can reveal in a unifying manner the detailed structure of quantum information. It may also enlighten the yet little explored interconnections of fundamental axiomatic properties within the deep structure of quantum mechanics.
A simultaneous realization of the universal optimal quantum cloning machine and of the universal-NOT gate by a quantum injected optical parametric amplification, is reported. The two processes, forbidden in their exact form for fundamental quantum limitations, are found universal and optimal, and the measured fidelity F<1 is found close to the limit values evaluated by quantum theory. This work may enlighten the yet little explored interconnections of fundamental axiomatic properties within the deep structure of quantum mechanics.