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Journal of the European Optical Society Rapid Publications

Quantum conditional cloning of continuous variable entangled states

K. Liu, Jiangrui Gao

Published Jan 1, 2014• 0 citations
Publisher

Abstract

We extend the technique of conditional preparation to a quantum cloning machine, and present a protocol of 1 → 2 conditional cloning of squeezed state and entanglement states. It is shown that the entanglement degree of the cloned entangled states can be well preserved even when the fidelity between the input and output states is beyond the limit of 4/9. This scheme is practicable since only the linear elements of beam splitters, homodyne detections, optical modulations and electrical trigger system, are involved.

DOI
10.2971/jeos.2014.14057

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We extend the technique of conditional preparation to a quantum cloning machine, and present a protocol of 1 → 2 conditional cloning of squeezed state and entanglement states. It is shown that the entanglement degree of the cloned entangled states can be well preserved even when the fidelity between the input and output states is beyond the limit of 4/9. This scheme is practicable since only the linear elements of beam splitters, homodyne detections, optical modulations and electrical trigger system, are involved.
We consider the quantum cloning of continuous variable entangled states. This is achieved by introducing two symmetric entanglement cloning machines (or eee-cloners): a local eee-cloner and a global eee-cloner; where we look at the preservation of entanglement in the clones under the condition that the fidelity of the clones is maximized. These cloning machines are implemented using simple linear optical elements such as beam splitters and homodyne detection along with squeeze gates. We show that the global eee-cloner out-performs the local eee-cloner both in terms of the fidelity of the cloned states as well as the strength of the entanglement of the clones. There is a minimum strength of entanglement (3 dB using the inseparability criterion) of the input state of the global eee-cloner that is required to preserve the entanglement in the clones.
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.
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.
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.
We investigate the performance of a selective cloning machine based on linear optical elements and Gaussian measurements, which allows one to clone at will one of the two incoming input states. This machine is a complete generalization of a $1\ensuremath{\rightarrow}2$ cloning scheme demonstrated by Andersen et al. [Phys. Rev. Lett. 94, 240503 (2005)]. The input-output fidelity is studied for a generic Gaussian input state, and the effect of nonunit quantum efficiency is also taken into account. We show that, if the states to be cloned are squeezed states with known squeezing parameter, then the fidelity can be enhanced using a third suitable squeezed state during the final stage of the cloning process. A binary communication protocol based on the selective cloning machine is also discussed.