Optimal cloning of mixed Gaussian states

Abstract

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.

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

References in corpus (4)

• The optimal cloning of quantum coherent states is non-Gaussian
• Asymptotic quantum cloning is state estimation
• Local asymptotic normality for qubit states
• Superbroadcasting of continuous variables mixed states

Cited by in corpus (9)

• Quantum Cloning Machines and the Applications
• Local asymptotic normality in quantum statistics
• Fidelity criterion for quantum-domain transmission and storage of coherent states beyond unit-gain constraint
• Quantum teleportation benchmarks for independent and identically-distributed spin states and displaced thermal states
• Fundamental quantum limits for practical devices
• Quantum steering as a resource for secure tripartite Quantum State Sharing
• Asymptotically optimal purification and dilution of mixed qubit and Gaussian states
• Amplification uncertainty relation for probabilistic amplifiers
• Asymptotically optimal quantum channel reversal for qudit ensembles and multimode Gaussian states