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arXiv:quant-ph/0612157 · Physical Review A

Continuous-variable quantum cloning of coherent states with phase-conjugate input modes using linear optics

Haixia Chen, Jing Zhang

Published Feb 7, 2007• 17 citations
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Abstract

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 $M$ identical optimal clones from $N$ replicas of a coherent state and $N$ 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.

DOI
10.1103/physreva.75.022306

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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.
An unknown quantum state is prohibited from perfect cloning due to the principles of quantum mechanics, while approximate cloning of an unknown quantum state can be achieved by constructing quantum cloning machines. In the continuous variable regime, to effectively improve the cloning fidelity, an N + N ′ → M + M ′ phase-conjugate inputs (PCI) quantum cloning scheme is proposed based on an optical parametric amplifier and beam splitter network. However, due to the difficulties in constructing an optical parametric amplifier approaching the quantum noise limit, such quantum cloning scheme has not been experimentally realized. In this work, we present all-optical N + N ′ → M + M ′ PCI quantum cloning of coherent states by utilizing a phase-sensitive amplifier based on a four-wave mixing process. In particular, we experimentally realize deterministic all-optical 1+1→ M + M ′ ( M = M ′ =2, 4) and 2+2→ M + M ′ ( M = M ′ =3, 4, 6, 8) PCI quantum cloning. The maximum cloning fidelities experimentally achieved are 96.76 % ±0.57 % and 96.80 % ±0.58 % in the 2+2→3+3 case, which are the maximum cloning fidelities in deterministic continuous variable quantum cloning, to our knowledge. Our results provide an effective scheme for enhancing cloning fidelity and can find applications in achieving high-fidelity quantum information protocols.
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.
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.
A quantum cloning machine is introduced that yields MMM identical optimal clones from NNN replicas of a coherent state and ${N}^{\ensuremath{'}}$ replicas of its phase conjugate. It also optimally produces ${M}^{\ensuremath{'}}{\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}M+N}^{\ensuremath{'}}\ensuremath{-}N$ phase-conjugate clones at no cost. For well chosen ratios ${N}^{\ensuremath{'}}/N$, this machine is shown to provide better cloning fidelities than the standard $({N+N}^{\ensuremath{'}})\ensuremath{\rightarrow}M$ cloner. The special cases of the optimal balanced cloner $({N\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}N}^{\ensuremath{'}})$ and optimal measurement $(M\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}\ensuremath{\infty})$ are investigated.