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arXiv:quant-ph/0401036 · Physical Review A

Conditional implementation of an asymmetrical universal quantum cloning machine

Radim Filip

Published Mar 16, 2004• 19 citations
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Abstract

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.

DOI
10.1103/physreva.69.032309

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We propose two feasible experimental implementations of an optimal asymmetric 1\ensuremath→21\ensuremath{\rightarrow}21\ensuremath→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.
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.
We report on experimental implementation of the optimal universal asymmetric $1\ensuremath{\rightarrow}2$ quantum cloning machine for qubits encoded into polarization states of single photons. Our linear-optical machine performs asymmetric cloning by partially symmetrizing the input polarization state of signal photon and a blank copy idler photon prepared in a maximally mixed state. We show that the employed method of measurement of mean clone fidelities exhibits strong resilience to imperfect calibration of the relative efficiencies of single-photon detectors used in the experiment. Reliable characterization of the quantum cloner is thus possible even when precise detector calibration is difficult to achieve.
Quantum cloning relates to the security of quantum computation and quantum communication. In this paper, firstly we propose a feasible unified scheme to implement optimal 1 → 2 universal, 1 → 2 asymmetric and symmetric phase-covariant cloning, and 1 → 2 economical phase-covariant quantum cloning machines only via a beam splitter. Then 1 → 3 economical phase-covariant quantum cloning machines also can be realized by adding another beam splitter in context of linear optics. The scheme is based on the interference of two photons on a beam splitter with different splitting ratios for vertical and horizontal polarization components. It is shown that under certain condition, the scheme is feasible by current experimental technology.
We propose an experimentally unified linear optical scheme to implement the optimal symmetric one to two (1 → 2) universal, optimal symmetric 1 → 2 phase-covariant and optimal symmetric economical one to three (1 → 3) phase-covariant quantum cloning machines of the polarization state of the single photon. This scheme requires single-photon sources as the input state. Here, we use a laser beam attenuated to the single-photon level as the input source. The scheme relies on one polarized qubit and two location qubits and it also involves linear optical elements. It is shown that under certain conditions, the scheme is feasible by current experimental technology.
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.
We propose two simple implementations of the optimal symmetric $\stackrel{\ensuremath{\rightarrow}}{1}2$ phase-covariant cloning machine for qubits. The first scheme is designed for qubits encoded into polarization states of photons and it involves a mixing of two photons on an unbalanced beam splitter. This scheme is probabilistic and the cloning succeeds with the probability 1/3.1/3.1/3. In the second setup, the qubits are represented by the states of Rydberg atoms and the cloning is accomplished by the resonant interaction of the atoms with a microwave field confined in a high-Q cavity. This latter approach allows for deterministic implementation of the optimal cloning transformation.