The fidelity for cloning coherent states is improved over that provided by optimal Gaussian and non-Gaussian cloners for the subset of coherent states that are prepared with known phases. Gaussian quantum cloning duplicates all coherent states with an optimal fidelity of $2∕3$ . Non-Gaussian cloners give optimal single-clone fidelity for a symmetric 1-to-2 cloner of 0.6826. Coherent states that have known phases can be cloned with a fidelity of $4∕5$ . The latter is realized by a combination of two beam splitters and a four-wave mixer operated in the nonlinear regime, all of which are realized by interaction Hamiltonians that are quadratic in the photon operators. Therefore, the known Gaussian devices for cloning coherent states are extended when cloning coherent states with known phases by considering a nonbalanced beam splitter at the input side of the amplifier.The fidelity for cloning coherent states is improved over that provided by optimal Gaussian and non-Gaussian cloners for the subset of coherent states that are prepared with known phases. Gaussian quantum cloning duplicates all coherent states with an optimal fidelity of $2∕3$. Non-Gaussian cloners give optimal single-clone fidelity for a symmetric 1-to-2 cloner of 0.6826. Coherent states that have known phases can be cloned with a fidelity of $4∕5$. The latter is realized by a combination of two beam splitters and a four-wave mixer operated in the nonlinear regime, all of which are realized by interaction Hamiltonians that are quadratic in the photon operators. Therefore, the known Gaussian devices for cloning coherent states are extended when cloning coherent states with known phases by considering a nonbalanced beam splitter at the input side of the amplifier.

Physical Review AApr 18, 20068 citations

Optimal Gaussian $N$ -to- $M$ cloning with linear optics and Gaussian cloning of known-phase coherent statesOptimal Gaussian $N$-to-$M$ cloning with linear optics and Gaussian cloning of known-phase coherent states

Ryo Namiki, Masato Koashi, Nobuyuki Imoto

We show how to implement the optimal Gaussian $N$ -to- $M$ cloning with linear optics and homodyne detection. We also show that the Gaussian $N$ -to- $M$ cloning of known-phase coherent states can be performed with the fidelity $\sqrt \frac{2 M N}{2M N+M -N}$ by linear optics and homodyne detection, and with $\frac{2}{\sqrt{1+\frac{1}{N}}+\sqrt {1-\frac{1}{M}}}$ by utilizing quadrature squeezing. From the classical limit of the cloning (1-to- $\infty$ cloning), a necessary condition of continuous variable quantum key distribution using known-phase coherent states is provided.We show how to implement the optimal Gaussian $N$-to-$M$ cloning with linear optics and homodyne detection. We also show that the Gaussian $N$-to-$M$ cloning of known-phase coherent states can be performed with the fidelity $\sqrt \frac{2 M N}{2M N+M -N}$ by linear optics and homodyne detection, and with $\frac{2}{\sqrt{1+\frac{1}{N}}+\sqrt {1-\frac{1}{M}}}$ by utilizing quadrature squeezing. From the classical limit of the cloning (1-to-$\infty$ cloning), a necessary condition of continuous variable quantum key distribution using known-phase coherent states is provided.

arXiv:quant-ph/0609170Sep 22, 20060 citations

Economical Gaussian cloning of coherent states with known phase

Yuli Dong, Xu‐Bo Zou, Shangbin Li +1 more

We investigate the economical Gaussian cloning of coherent states with the known phase, which produces $M$ copies from $N$ input replica and can be implemented with degenerate parametric amplifiers and beam splitters.The achievable fidelity of single copy is given by $2M\sqrt{N}∕[\sqrt{N}(M\ensuremath{-}1)+\sqrt{(1+N)({M}^{2}+N)}]$, which is bigger than the optimal fidelity of the universal Gaussian cloning. The cloning machine presented here works without ancillary optical modes and can be regarded as the continuous variable generalization of the economical cloning machine for qudits.We investigate the economical Gaussian cloning of coherent states with the known phase, which produces $M$ copies from $N$ input replica and can be implemented with degenerate parametric amplifiers and beam splitters.The achievable fidelity of single copy is given by $2M\sqrt{N}∕[\sqrt{N}(M\ensuremath{-}1)+\sqrt{(1+N)({M}^{2}+N)}]$, which is bigger than the optimal fidelity of the universal Gaussian cloning. The cloning machine presented here works without ancillary optical modes and can be regarded as the continuous variable generalization of the economical cloning machine for qudits.

Physical Review AJul 9, 20076 citations

Conservation of Gaussian distributions of coherent states

H. Robl

Physics Letters AFeb 1, 19673 citations

2∕3

. Non-Gaussian cloners give optimal single-clone fidelity for a symmetric 1-to-2 cloner of 0.6826. Coherent states that have known phases can be cloned with a fidelity of

4∕5

. The latter is realized by a combination of two beam splitters and a four-wave mixer operated in the nonlinear regime, all of which are realized by interaction Hamiltonians that are quadratic in the photon operators. Therefore, the known Gaussian devices for cloning coherent states are extended when cloning coherent states with known phases by considering a nonbalanced beam splitter at the input side of the amplifier.

Optimal Gaussian

N

-to-

M

cloning with linear optics and Gaussian cloning of known-phase coherent states

We show how to implement the optimal Gaussian

N

-to-

M

cloning with linear optics and homodyne detection. We also show that the Gaussian

N

-to-

M

cloning of known-phase coherent states can be performed with the fidelity

\sqrt \frac{2 M N}{2M N+M -N}

by linear optics and homodyne detection, and with

\frac{2}{\sqrt{1+\frac{1}{N}}+\sqrt {1-\frac{1}{M}}}

by utilizing quadrature squeezing. From the classical limit of the cloning (1-to-

\infty

cloning), a necessary condition of continuous variable quantum key distribution using known-phase coherent states is provided.

We investigate the economical Gaussian cloning of coherent states with the known phase, which produces

M

copies from

N

input replica and can be implemented with degenerate parametric amplifiers and beam splitters.The achievable fidelity of single copy is given by $2M\sqrt{N}∕[\sqrt{N}(M\ensuremath{-}1)+\sqrt{(1+N)({M}^{2}+N)}]$, which is bigger than the optimal fidelity of the universal Gaussian cloning. The cloning machine presented here works without ancillary optical modes and can be regarded as the continuous variable generalization of the economical cloning machine for qudits.