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arXiv:quant-ph/0501005 · Physical Review Letters

Unconditional Quantum Cloning of Coherent States with Linear Optics

Ulrik L. Andersen, Vincent Josse, Gerd Leuchs

Published Jun 24, 2005• 114 citations
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Abstract

A scheme for optimal Gaussian cloning of optical coherent states is proposed and experimentally demonstrated. Its optical realization is based entirely on simple linear optical elements and homodyne detection. The optimality of the presented scheme is limited only by detection inefficiencies. Experimentally, we achieved a cloning fidelity of about 65%, which almost touches the optimal value of $2/3$.

DOI
10.1103/physrevlett.94.240503

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A scheme for optimal Gaussian cloning of optical coherent states is proposed and experimentally demonstrated. Its optical realization is based entirely on simple linear optical elements and homodyne detection. The optimality of the presented scheme is limited only by detection inefficiencies. Experimentally, we achieved a cloning fidelity of about 65%, which almost touches the optimal value of 2/32/32/3.
In this chapter we present a scheme for optimal Gaussian cloning of optical coherent states. Its optical realization is based entirely on simple linear optical elements and homodyne detection. This is in contrast to previous proposals where parametric processes were suggested to be used for optimal Gaussian cloning. The optimality of the presented scheme is only limited by detection inefficiencies. Experimentally we achieved a cloning fidelity of up to 65%, which almost touches the optimal value of 2/3.
Optimal Gaussian NNN-to-MMM cloning with linear optics and Gaussian cloning of known-phase coherent states
We show how to implement the optimal Gaussian NNN-to-MMM cloning with linear optics and homodyne detection. We also show that the Gaussian NNN-to-MMM cloning of known-phase coherent states can be performed with the fidelity 2MN2MN+M−N\sqrt \frac{2 M N}{2M N+M -N}2MN+M−N2MN​​ by linear optics and homodyne detection, and with 21+1N+1−1M\frac{2}{\sqrt{1+\frac{1}{N}}+\sqrt {1-\frac{1}{M}}}1+N1​​+1−M1​​2​ by utilizing quadrature squeezing. From the classical limit of the cloning (1-to-∞\infty∞ cloning), a necessary condition of continuous variable quantum key distribution using known-phase coherent states is provided.
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.
We analyze in details a scheme for cloning of Gaussian states based on linear optical components and homodyne detection recently demonstrated by Andersen et al. [Phys. Rev. Lett. 94, 240503 (2005)]. The input-output fidelity is evaluated for a generic (pure or mixed) Gaussian state taking into account the effect of nonunit quantum efficiency and unbalanced mode mixing. In addition, since in most quantum information protocols the covariance matrix of the set of input states is not perfectly known, we evaluate the average cloning fidelity for classes of Gaussian states with the degree of squeezing and the number of thermal photons being only partially known.
We consider the optimal cloning of quantum coherent states with single-clone and joint fidelity as figures of merit. While the latter is maximized by a Gaussian cloner, the former is not: the optimal single-clone fidelity for a symmetric 1-to-2 cloner is 0.6826, compared to 2/3 in a Gaussian setting. This cloner can be realized with an optical parametric amplifier and certain non-Gaussian bimodal states. Finally, we show that the single-clone fidelity of the optimal 1-to-infinity cloner is 1/2. It is achieved by a Gaussian scheme and cannot be surpassed even with supplemental bound entangled states.