Optimal<b><i>N</i></b>-to-<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>M</mml:mi></mml:math>cloning of conjugate quantum variables

Cerf, Nicolas J.; Iblisdir, Sofyan

doi:10.1103/physreva.62.040301

Cited by 112 publications

(119 citation statements)

References 19 publications

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“…Cloning of coherent states in an infinite dimensional space was considered in [10,11], where transformation for cloning of all coherent states with the same fidelity F = 2/3 was proposed. A proof that such a cloning procedure gives the highest possible fidelity for coherent states was later given in [12].…”

Section: Introductionmentioning

confidence: 99%

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Cloning of spin-coherent states

2004

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We consider optimal cloning of the spin coherent states in Hilbert spaces of different dimensionality d. We give explicit form of optimal cloning transformation for spin coherent states in the threedimensional space, analytical results for the fidelity of the optimal cloning in d = 3 and d = 4 as well as numerical results for higher dimensions. In the low-dimensional case we construct the corresponding completely positive maps and exhibit their structure with the help of Jamio lkowski isomorphism. This allows us to formulate some conjectures about the form of optimal coherent cloning CP maps in arbitrary dimension.

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Section: Introductionmentioning

confidence: 99%

“…Instead of the optimization scheme, the authors of [12] make use of limitations on so called joint measurement [13]. The idea of joint measurement is to perform some kind of a measurement on a quantum system that would give us simultaneously some information about two noncommuting observables (for example position and momentum).…”

Section: Introductionmentioning

confidence: 99%

Cloning of spin-coherent states

2004

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“…Originally, such a machine was proposed for cloning of qubits and has later been demonstrated experimentally [6]. Shortly after this development, a continuous variable (CV) [7] analog of the qubit quantum cloner was proposed [8,9] and recently it was shown that a CV optimal Gaussian cloner of coherent states can be implemented using an appropriate combination of beam splitters and a single phase insensitive parametric amplifier [10,11]. Although this proposal sounds experimentally promising, the implementation of an efficient phase insensitive amplifier operating at the fundamental limit is a challenging task.…”

Section: Introductionmentioning

confidence: 99%

Cloning of Gaussian states by linear optics

2006

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We analyze in details a scheme for cloning of Gaussian states based on linear optical components and homodyne detection recently demonstrated by U. L. Andersen et al. [Phys. Rev. Lett. 94, 240503 (2005)]. The input-output fidelity is evaluated for a generic (pure or mixed) Gaussian state taking into account the effect of non-unit quantum efficiency and unbalanced mode-mixing. In addition, since in most quantum information protocols the covariance matrix of the set of input states is not perfectly known, we evaluate the average cloning fidelity for classes of Gaussian states with the degree of squeezing and the number of thermal photons being only partially known.

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“…Problems in quantum information such as entanglement measures [16] and quantum channels [17] have been partially solved by restricting to the framework of Gaussian states and operations. For coherent states the optimal cloning problem has been investigated in [18,19,20] under the restriction of Gaussian transformation. The question whether the optimal cloning map is indeed Gaussian has been answered positively in the case of global figure of merit with fidelity, and negatively for the individual figure of merit [21] .…”

Section: Introductionmentioning

confidence: 99%

Optimal cloning of mixed Gaussian states

Guţǎ

Matsumoto

2006

Phys. Rev. A

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We construct the optimal 1 to 2 cloning transformation for the family of displaced thermal equilibrium states of a harmonic oscillator, with a fixed and known temperature. The transformation is Gaussian and it is optimal with respect to the figure of merit based on the joint output state and norm distance. The proof of the result is based on the equivalence between the optimal cloning problem and that of optimal amplification of Gaussian states which is then reduced to an optimization problem for diagonal states of a quantum oscillator. A key concept in finding the optimum is that of stochastic ordering which plays a similar role in the purely classical problem of Gaussian cloning. The result is then extended to the case of n to m cloning of mixed Gaussian states.

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OptimalN-to-Mcloning of conjugate quantum variables

Cited by 112 publications

References 19 publications

Cloning of spin-coherent states

Cloning of spin-coherent states

Cloning of Gaussian states by linear optics

Optimal cloning of mixed Gaussian states

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