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Physical Review A

Linear optical implementation of ancilla-free 1→3 optimal phase covariant quantum cloning machines for the equatorial qubits

Xu‐Bo Zou, Wolfgang M. Mathis

Published Aug 8, 2005• 21 citations
Publisher

Abstract

We propose experimental schemes to implement ancilla-free $1\ensuremath{\rightarrow}3$ optimal phase covariant quantum cloning machines for $x\text{\ensuremath{-}}y$ and $x\text{\ensuremath{-}}z$ equatorial qubits by interfering a polarized photon, which we wish to clone, with different light resources at a six-port symmetric beam splitter. The scheme requires linear optical elements and three-photon coincidence detection, and is feasible with current experimental technology.

DOI
10.1103/physreva.72.022306

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We experimentally realize the $1\ensuremath{\rightarrow}2$ optimal universal quantum cloning machine for arbitrary qubits and the ancilla-free $1\ensuremath{\rightarrow}3$ optimal phase-covariant quantum cloning machine for $x\text{\ensuremath{-}}y$ equatorial qubits, which were constructed by Zou et al. [Phys. Lett. A 366, 36 (2007)]. The qubits are represented by the polarization states of photons prepared from the process of spontaneous parametric down-conversion. The copies of each machine are shown to have almost equal fidelities conditioned on fourfold coincidences.
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In this paper we report an experimental realization of an ancilla-free $1\ensuremath{\rightarrow}2$ phase-covariant quantum cloner. The cloner is realized by interfering a linearly polarized photon, which we wish to clone with a circularly polarized photon at a beam splitter. The two-photon effect can be understood in light of Hong-Ou-Mandel interference. The fidelity of the cloner was measured as $0.829\ifmmode\pm\else\textpm\fi{}0.008$ for the 0∕900∕900∕90 basis and $0.835\ifmmode\pm\else\textpm\fi{}0.006$ for the 45∕13545∕13545∕135 basis, which is in good agreement with the theoretical prediction of 5∕65∕65∕6 fidelity. The experimental scheme is straightforward and has a high cloning success rate.
We report on two optical realizations of the $1\ensuremath{\rightarrow}2$ asymmetric phase-covariant cloning machines for polarization states of single photons. The experimental setups combine two-photon interference and tunable polarization filtering, which enables us to control the asymmetry of the cloners. The first scheme involves a special unbalanced bulk beam splitter exhibiting different splitting ratios for vertical and horizontal polarizations, respectively. The second implemented scheme consists of a balanced fiber coupler where photon bunching occurs, followed by a free-space part with polarization filters. With this latter approach we were able to demonstrate very high cloning fidelities which are above the universal cloning limit.