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Cloning of continuous quantum variables

Cerf1, Ipe, Rottenberg

  • 1Ecole Polytechnique, CP 165, Universite Libre de Bruxelles, 1050 Brussels, Belgium and Information and Computing Technologies Research Section, Jet Propulsion Laboratory, California Institute of Technology, Pasadena, California 91109, USA.

Physical Review Letters
|September 6, 2000
PubMed
Summary

This study analyzes quantum cloning for continuous variables, presenting a Gaussian cloning machine that copies conjugate variables like position and momentum. The machine achieves a 2/3 fidelity for coherent states and ensures copies obey a no-cloning uncertainty relation.

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Area of Science:

  • Quantum Information Science
  • Quantum Mechanics
  • Quantum Optics

Background:

  • The no-cloning theorem is a fundamental principle in quantum mechanics, prohibiting the perfect cloning of an arbitrary unknown quantum state.
  • Quantum cloning machines aim to create approximate copies of quantum states, which has implications for quantum communication and computation.

Purpose of the Study:

  • To analyze the cloning of quantum variables with continuous spectra.
  • To introduce and evaluate a Gaussian quantum cloning machine for conjugate variables.

Main Methods:

  • Theoretical analysis of quantum cloning protocols.
  • Development of a Gaussian quantum cloning machine model.
  • Fidelity calculations for state duplication.

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Main Results:

  • A Gaussian quantum cloning machine is presented that equally copies states of conjugate variables (e.g., position and momentum).
  • The machine duplicates all coherent states with a fidelity of 2/3.
  • The cloned states were shown to obey a no-cloning Heisenberg-like uncertainty relation.

Conclusions:

  • The developed Gaussian cloning machine provides a practical approach to approximate quantum state duplication for continuous variables.
  • The findings contribute to understanding the limits of quantum information processing and the trade-offs inherent in quantum cloning.