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Physical Review Letters

All-Optical Optimal N -to- M Quantum Cloning of Coherent States

Shengshuai Liu, Yanbo Lou, Yingxuan Chen, Jietai Jing

Published Feb 10, 2021• 26 citations

Abstract

The laws of quantum mechanics forbid the perfect copying of an unknown quantum state, known as the no-cloning theorem. In spite of this, approximate cloning with imperfect fidelity is possible, which opens up the field of quantum cloning. In general, quantum cloning can be divided into discrete variable and continuous variable (CV) categories. In the CV regime, all-optical implementation of the optimal N→M quantum cloning has been proposed in two original parallel works, which involves a parametric amplifier and a set of beam splitters and thus avoids the optic-electro and electro-optic conversions in the current CV quantum cloning technologies. However, such original proposal of all-optical CV optimal N→M quantum cloning scheme has never been experimentally implemented. Here, we show that optimal N→M quantum cloning of coherent states can be realized by utilizing a parametric amplifier based on four-wave mixing process in a hot atomic vapor and a set of beam splitters. In particular, we realize 1→M, 2→M, and 4→M quantum cloning. We find that the fidelity of N→M quantum cloning increases with the decrease of clone number M and the increase of original replica number N. The best cloning fidelity achieved in our experiment is about 93.3% ±1.0% in the 4→5 case. Our results may find potential applications in realizing all-optical high-fidelity quantum state transfer and all-optical high-compatibility eavesdropping attack in quantum communication networks.

DOI: 10.1103/physrevlett.126.060503

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An unknown quantum state is prohibited from perfect cloning due to the principles of quantum mechanics, while approximate cloning of an unknown quantum state can be achieved by constructing quantum cloning machines. In the continuous variable regime, to effectively improve the cloning fidelity, an N + N ′ → M + M ′ phase-conjugate inputs (PCI) quantum cloning scheme is proposed based on an optical parametric amplifier and beam splitter network. However, due to the difficulties in constructing an optical parametric amplifier approaching the quantum noise limit, such quantum cloning scheme has not been experimentally realized. In this work, we present all-optical N + N ′ → M + M ′ PCI quantum cloning of coherent states by utilizing a phase-sensitive amplifier based on a four-wave mixing process. In particular, we experimentally realize deterministic all-optical 1+1→ M + M ′ ( M = M ′ =2, 4) and 2+2→ M + M ′ ( M = M ′ =3, 4, 6, 8) PCI quantum cloning. The maximum cloning fidelities experimentally achieved are 96.76 % ±0.57 % and 96.80 % ±0.58 % in the 2+2→3+3 case, which are the maximum cloning fidelities in deterministic continuous variable quantum cloning, to our knowledge. Our results provide an effective scheme for enhancing cloning fidelity and can find applications in achieving high-fidelity quantum information protocols.

Cloning machines, that is, transformations that achieve the best approximate copying of a quantum state compatible with the no-cloning theorem, have been a fundamental research topic over the last five years. This study is of particular significance given the close connection between quantum cloning and quantum cryptography: using an optimal cloner generally makes it possible to obtain a tight bound on the best individual eavesdropping strategy in a quantum cryptosystem. In this Chapter, the issue of cloning a continuous-variable quantum system will be analyzed, and a Gaussian cloning transformation will be introduced. This cloner, which copies equally well any two canonically conjugate continuous variables, duplicates all coherent states with a same fidelity (F=2/3). The optical implementation of this cloner and its extension to N-to-M cloners will also be discussed. Finally, the use of this cloner for the security assessment of a quantum key distribution scheme relying on continuous (Gaussian) key carriers will be sketched.

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

M

identical optimal clones from

N

replicas of a coherent state and

N

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.