Optimal cloning of mixed Gaussian states

Details Optimal cloning of mixed Gaussian states Optimal cloning of mixed Gaussian states

2006-05-18

arxiv.org/abs/quant-ph/0605161v2

Phys. Rev A, 74, 032305 (2006)

Physics

Quantum Physics

8 pages, 1 figure; proof of general form of covariant amplifiers added

Scientific paper

10.1103/PhysRevA.74.032305

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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