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arXiv:quant-ph/0612132 · Physical Review A

Experimental realization of 1→2 asymmetric phase-covariant quantum cloning

Hongwei Chen, Xianyi Zhou, Dieter Suter, Jiangfeng Du

Published Jan 17, 2007• 69 citations
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Abstract

While exact cloning of an unknown quantum state is prohibited by the linearity of quantum mechanics, approximate cloning is possible and has been used, e.g., to derive limits on the security of quantum communication protocols. In the case of asymmetric cloning, the information from the input state is distributed asymmetrically between the different output states. Here, we consider asymmetric phase-covariant cloning, where the goal is to optimally transfer the phase information from a single input qubit to different output qubits. We construct an optimal quantum cloning machine for two qubits that does not require ancilla qubits and implement it on an NMR quantum information processor.

DOI
10.1103/physreva.75.012317

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While exact cloning of an unknown quantum state is prohibited by the linearity of quantum mechanics, approximate cloning is possible and has been used, e.g., to derive limits on the security of quantum communication protocols. In the case of asymmetric cloning, the information from the input state is distributed asymmetrically between the different output states. Here, we consider asymmetric phase-covariant cloning, where the goal is to optimally transfer the phase information from a single input qubit to different output qubits. We construct an optimal quantum cloning machine for two qubits that does not require ancilla qubits and implement it on an NMR quantum information processor.
In several quantum information (QI) phenomena of large technological importance the information is carried by the phase of the quantum superposition states, or qubits. The phase-covariant cloning machine (PQCM) addresses precisely the problem of optimally copying these qubits with the largest attainable ``fidelity.'' We present a general scheme which realizes the $1\ensuremath{\rightarrow}3$ phase covariant cloning process by a combination of three different QI processes: the universal cloning, the NOT gate, and the projection over the symmetric subspace of the output qubits. The experimental implementation of a PQCM for polarization encoded qubits, the first ever realized with photons, is reported.
The optimal phase-covariant quantum cloning machine (PQCM) broadcasts the information associated to an input qubit into a multiqubit system, exploiting a partial a priori knowledge of the input state. This additional a priori information leads to a higher fidelity than for the universal cloning. The present article first analyzes different innovative schemes to implement the $1\ensuremath{\rightarrow}3$ PQCM. The method is then generalized to any $1\ensuremath{\rightarrow}M$ machine for an odd value of MMM by a theoretical approach based on the general angular momentum formalism. Finally different experimental schemes based either on linear or nonlinear methods and valid for single photon polarization encoded qubits are discussed.
No-cloning theorem is fundamental for quantum mechanics and for quantum information science that states an unknown quantum state cannot be cloned perfectly. However, we can try to clone a quantum state approximately with the optimal fidelity, or instead, we can try to clone it perfectly with the largest probability. Thus various quantum cloning machines have been designed for different quantum information protocols. Specifically, quantum cloning machines can be designed to analyze the security of quantum key distribution protocols such as BB84 protocol, six-state protocol, B92 protocol and their generalizations. Some well-known quantum cloning machines include universal quantum cloning machine, phase-covariant cloning machine, the asymmetric quantum cloning machine and the probabilistic quantum cloning machine etc. In the past years, much progress has been made in studying quantum cloning machines and their applications and implementations, both theoretically and experimentally. In this review, we will give a complete description of those important developments about quantum cloning and some related topics. On the other hand, this review is self-consistent, and in particular, we try to present some detailed formulations so that further study can be taken based on those results.
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 present a scheme to realize a special quantum cloning machine via input-output cavities. The cloning machine can copy information from one atom to another distant atom. Choosing different parameters, the method can perform optimal symmetric (asymmetric) universal quantum cloning and optimal symmetric (asymmetric) phase-covariant cloning. Compared to previous schemes, our scheme is more insensitive to actual environmental noise and can get higher fidelity in a current cavity quantum electrodynamics system with an entangled state acting as a quantum channel than a single-photon pulse.
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.