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arXiv:quant-ph/0512002 · New Journal of Physics

Optimal cloning of single-photon polarization by coherent feedback of beam splitter losses

Holger F Hofmann, Toshiki Ide

Published Aug 7, 2006• 2 citations
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Abstract

Light fields can be amplified by measuring the field amplitude reflected at a beam splitter of reflectivity R and adding a coherent amplitude proportional to the measurement result to the transmitted field. By applying the quantum optical realization of this amplification scheme to single-photon inputs, it is possible to clone the polarization states of photons. We show that optimal cloning of single-photon polarization is possible when the gain factor of the amplification is equal to .

DOI
10.1088/1367-2630/8/8/130

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Light fields can be amplified by measuring the field amplitude reflected at a beam splitter of reflectivity R and adding a coherent amplitude proportional to the measurement result to the transmitted field. By applying the quantum optical realization of this amplification scheme to single-photon inputs, it is possible to clone the polarization states of photons. We show that optimal cloning of single-photon polarization is possible when the gain factor of the amplification is equal to .
Light fields can be amplified by measuring the field amplitude reflected at a beam splitter of reflectivity R and adding a coherent amplitude proportional to the measurement result to the transmitted field. By applying the quantum optical realization of this amplification scheme to single photon inputs, it is possible to clone the polarization states of photons. We show that optimal cloning of single photon polarization is possible when the gain factor of the amplification is equal to the inverse squareroot of 1-R.
We demonstrate how a beam splitter in combination with different light sources can be used as an optimal universal 1-->2 quantum cloner and as an optimal universal quantum NOT machine for the polarization qubit of a single photon. For the cloning a source of single photons with maximally mixed polarization is required and for the NOT operation a source of maximally entangled photon pairs. We demonstrate both operations with near optimal fidelity. Our scheme can be generalized in a natural way to clone and NOT the spin state of electrons.
A linear optical probabilistic scheme for the optimal cloning of a pair of orthogonally polarized photons is devised, based on single- and two-photon interferences. It consists in a partial symmetrization device realized with a modified unbalanced Mach-Zehnder interferometer, followed by two balanced beam splitters where the Hong-Ou-Mandel photon bunching occurs. This scheme has the advantage that it enables quantum cloning without the need for stimulated amplification in a nonlinear medium. It can also be modified so to make an optical two-qubit partial SWAP gate, thereby providing a potentially useful tool to linear optics quantum computing.
We propose two feasible experimental implementations of an optimal asymmetric $1\ensuremath{\rightarrow}2$ quantum cloning of a polarization state of photon. Both implementations are based on a partial and optimal reverse of recent conditional symmetrical quantum cloning experiments. The reversion procedure is performed only by a local measurement of one from the clones and ancilla followed by a local operation on the other clone. The local measurement consists only of a single unbalanced beam splitter followed in one output by a single-photon detector and the asymmetry of fidelities in the cloning is controlled by a reflectivity of the beam splitter.
The experimental realization of optimal symmetric phase-covariant $1\ensuremath{\rightarrow}2$ cloning of qubit states is presented. The qubits are represented by polarization states of photons generated by spontaneous parametric down-conversion. The experiment is based on the interference of two photons on a custom-made beam splitter with different splitting ratios for vertical and horizontal polarization components. From the measured data we have estimated the implemented cloning transformation using the maximum-likelihood method. The result shows that the realized transformation is very close to the ideal one and the map fidelity reaches 94%.