author={Reinhard F. Werner},
  journal={Physical Review A},
  • R. Werner
  • Published 1 April 1998
  • Mathematics
  • Physical Review A
We construct the unique optimal quantum device for turning a finite number of d-level quantum systems in the same unknown pure state \sigma into M systems of the same kind, in an approximation of the M-fold tensor product of the state \sigma. 
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On the Entanglement Structure in Quantum Cloning
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Optimal cloning of pure states, testing single clones
We consider quantum devices for turning a finite number N of d-level quantum systems in the same unknown pure state σ into M>N systems of the same kind, in an approximation of the M-fold tensor


Universal Algorithm for Optimal Estimation of Quantum States from Finite Ensembles via Realizable Ge
A universal algorithm for the optimal quantum state estimation of an arbitrary finite dimensional system that specifies a physically realizable positive operator valued measurement on a finite number of identically prepared systems is presented.
Optimal extraction of information from finite quantum ensembles.
It is proved that optimal measurement procedures must necessarily view the ensemble as a single composite system rather than as the sum of its components, i.e., optimal measurements cannot be realized by separate measurements on each particle.
Optimal Quantum Cloning Machines
Quantum Cloning Machines (QCM) are universal devices to translate quantum information into classical information and it is proved that the fidelity (quality) of these copies is optimal.
Quantum copying: Beyond the no-cloning theorem.
  • Buzek, Hillery
  • Physics
    Physical review. A, Atomic, molecular, and optical physics
  • 1996
It is shown that there exists a ‘‘universal quantum-copying machine’’ ~i.e., transformation! which approximately copies quantum-mechanical states such that the quality of its output does not depend on the input.
Two non-orthogonal states can be cloned by a unitary-reduction process
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Classical mechanics as quantum mechanics with infinitesimal ħ
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Probabilistic and Statistical Aspects of Quantum Theory
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A single quantum cannot be cloned
If a photon of definite polarization encounters an excited atom, there is typically some nonvanishing probability that the atom will emit a second photon by stimulated emission. Such a photon is