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Classical no-cloning theorem.

A Daffertshofer1, A R Plastino, A Plastino

  • 1Faculty of Human Movement Sciences, Vrije Universiteit, van der Boechorststraat 9, 1081 BT, Amsterdam, The Netherlands. marlow@fbw.vu.nl

Physical Review Letters
|June 13, 2002
PubMed
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The no-cloning theorem prevents copying probability distributions in classical systems. Even with a copying machine, the original system

Area of Science:

  • Classical physics
  • Dynamical systems theory
  • Information theory

Background:

  • The no-cloning theorem is a fundamental principle in quantum mechanics.
  • Its implications for classical systems are less explored.
  • Understanding information preservation in classical systems is crucial.

Purpose of the Study:

  • To investigate a classical version of the no-cloning theorem.
  • To determine if arbitrary probability distributions can be cloned in classical systems.
  • To analyze the constraints imposed by classical dynamics on information copying.

Main Methods:

  • Analysis of classical dynamical systems.
  • Examination of Liouvillian (ensemble) evolution.
  • Consideration of joint probability distributions for composite systems.

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Main Results:

  • An arbitrary probability distribution from a source system cannot be perfectly copied to a target system.
  • The original source system's probability distribution remains unperturbed.
  • Liouvillian evolution inherently prevents perfect cloning in classical dynamical systems.

Conclusions:

  • The no-cloning theorem has a classical analogue.
  • Perfect information copying is impossible in classical dynamical systems.
  • Ensemble evolution dynamics enforce constraints on information duplication.