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Optical Fiber Communication Conference

Asymmetric continuous-variable cloning machine

Jaromı́r Fiurášek

Published Jan 1, 2001• 0 citations
Publisher

Abstract

I propose a simple optical implementation of asymmetric continuous variable quantum cloning machine which optimally clones coherent states. The cloning device consists of Mach-Zehnder interferometer with nondegenerate parametric amplifier placed in one of its arms.
DOI
10.1364/icqi.2001.pa8

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We propose a scheme for continuous-variable quantum cloning of coherent states with phase-conjugate input modes using linear optics. The quantum cloning machine yields MMM identical optimal clones from NNN replicas of a coherent state and NNN replicas of its phase conjugate. This scheme can be straightforwardly implemented with the setups accessible at present since its optical implementation only employs simple linear optical elements and homodyne detection. Compared with the original scheme for continuous-variable quantum cloning with phase-conjugate input modes proposed by Cerf and Iblisdir [Phys. Rev. Lett. 87, 247903 (2001)], which utilized a nondegenerate optical parametric amplifier, our scheme loses the output of phase-conjugate clones and is regarded as irreversible quantum cloning.
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.
The laws of quantum mechanics forbid the perfect copying of an unknown quantum state, known as the no-cloning theorem. In spite of this, approximate cloning with imperfect fidelity is possible, which opens up the field of quantum cloning. In general, quantum cloning can be divided into discrete variable and continuous variable (CV) categories. In the CV regime, all-optical implementation of the optimal N→M quantum cloning has been proposed in two original parallel works, which involves a parametric amplifier and a set of beam splitters and thus avoids the optic-electro and electro-optic conversions in the current CV quantum cloning technologies. However, such original proposal of all-optical CV optimal N→M quantum cloning scheme has never been experimentally implemented. Here, we show that optimal N→M quantum cloning of coherent states can be realized by utilizing a parametric amplifier based on four-wave mixing process in a hot atomic vapor and a set of beam splitters. In particular, we realize 1→M, 2→M, and 4→M quantum cloning. We find that the fidelity of N→M quantum cloning increases with the decrease of clone number M and the increase of original replica number N. The best cloning fidelity achieved in our experiment is about 93.3% ±1.0% in the 4→5 case. Our results may find potential applications in realizing all-optical high-fidelity quantum state transfer and all-optical high-compatibility eavesdropping attack in quantum communication networks.
We propose an asymmetric quantum cloning scheme. Based on the proposal and experiment by Andersen et al. [Phys. Rev. Lett. 94, 240503 (2005)], we generalize it to two asymmetric cases: quantum cloning with asymmetry between output clones and between quadrature variables. These optical implementations also employ linear elements and homodyne detection only. Finally, we also compare the utility of symmetric and asymmetric cloning in an analysis of a squeezed-state quantum key distribution protocol and find that the asymmetric one is more advantageous.