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Quantum Darwinism


Quantum Darwinism describes the proliferation, in the environment, of multiple records of selected states of a quantum system. It explains how the quantum fragility of a state of a single quantum system can lead to the classical robustness of states in their correlated multitude; shows how effective ‘wave-packet collapse’ arises as a result of the proliferation throughout the environment of imprints of the state of the system; and provides a framework for the derivation of Born’s rule, which relates the probabilities of detecting states to their amplitudes. Taken together, these three advances mark considerable progress towards settling the quantum measurement problem.

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Figure 1: Quantum Darwinism and the structure of the environment.
Figure 2: Information about stored in and its redundancy.
Figure 3: Quantum Darwinism in a simple model of decoherence12.
Figure 4: Probabilities and symmetry.


  1. Bohr, N. The quantum postulate and the recent development of atomic theory. Nature 121, 580–590 (1928).

    ADS  Article  Google Scholar 

  2. Schrödinger, E. Die gegenwärtige Situation in der Quantenmechanik. Naturwissenschaften 23, 807–812; 823–828; 844–849 (1935).

  3. Joos, E. et al. Decoherence and the Appearance of a Classical World in Quantum Theory (Springer, 2003).

    Book  Google Scholar 

  4. Zurek, W. H. Decoherence, einselection, and the quantum origins of the classical. Rev. Mod. Phys. 75, 715–775 (2003).

    ADS  MathSciNet  Article  Google Scholar 

  5. Schlosshauer, M. Decoherence and the Quantum-to-Classical Transition (Springer, 2007).

    Google Scholar 

  6. Zurek, W. H. Pointer basis of a quantum apparatus: Into what mixture does the wavepacket collapse? Phys. Rev. D 24, 1516–1525 (1981).

    ADS  MathSciNet  Article  Google Scholar 

  7. Zurek, W. H. Environment-induced superselection rules. Phys. Rev. D 26, 1862–1880 (1982).

    ADS  MathSciNet  Article  Google Scholar 

  8. Paz, J.-P. & Zurek, W. H. in Coherent Atomic Matter Waves, Les Houches Lectures (eds Kaiser, R., Westbrook, C. & David, F.) 533–614 (Springer, 2001).

    Book  Google Scholar 

  9. Zurek, W. H., Habib, S. & Paz, J.-P. Coherent states via decoherence. Phys. Rev. Lett. 70, 1187–1190 (1993).

    ADS  Article  Google Scholar 

  10. Tegmark, M. & Shapiro, H. S. Decoherence produces coherent states: An explicit proof for harmonic chains. Phys. Rev. E 50, 2538–2547 (1994).

    ADS  Article  Google Scholar 

  11. Gallis, M. R. The emergence of classicality via decoherence described by Lindblad operators. Phys. Rev. A 53, 655–660 (1996).

    ADS  MathSciNet  Article  Google Scholar 

  12. Ollivier, H., Poulin, D & Zurek, W. H. Objective properties from subjective quantum states: Environment as a witness. Phys. Rev. Lett. 93, 220401 (2004).

    ADS  Article  Google Scholar 

  13. Blume-Kohout, R. & Zurek, W. H. A simple example of quantum Darwinism: Redundant information storage in many-spin environments. Found. Phys. 35, 1857–1876 (2005).

    ADS  MathSciNet  Article  Google Scholar 

  14. Blume-Kohout, R. & Zurek, W. H. Quantum Darwinism: Entanglement, branches, and the emergent classicality of redundantly stored quantum information. Phys. Rev. A 73, 062310 (2006).

    ADS  Article  Google Scholar 

  15. Blume-Kohout, R. & Zurek, W. H. Quantum Darwinism in quantum Brownian motion. Phys. Rev. Lett. 101, 240405 (2008).

    ADS  MathSciNet  Article  Google Scholar 

  16. Zurek, W. H. Einselection and decoherence from an information theory perspective. Ann. Phys. 9, 855–864 (2000).

    MathSciNet  Article  Google Scholar 

  17. Born, M. Zur Quantenmechanik der Stossvorgänge. Zeits. Phys. 37, 863–867 (1926).

    ADS  Article  Google Scholar 

  18. Wootters, W. K. & Zurek, W. H. A single quantum cannot be cloned. Nature 299, 802–803 (1982).

    ADS  Article  Google Scholar 

  19. Dieks, D. Communication by EPR devices. Phys. Lett. A 92, 271–272 (1982).

    ADS  Article  Google Scholar 

  20. Dirac, P. A. M. Quantum Mechanics (Clarendon, 1958).

    MATH  Google Scholar 

  21. Zurek, W. H. Quantum origin of quantum jumps: Breaking of unitary symmetry induced by information transfer and the transition from quantum to classical. Phys. Rev. A 76, 052110 (2007).

    ADS  Article  Google Scholar 

  22. Ollivier, H., Poulin, D. & Zurek, W. H. Environment as a witness: Selective proliferation of information and emergence of objectivity in a quantum universe. Phys. Rev. A 72, 423113 (2005).

    Article  Google Scholar 

  23. Nielsen, M. A. & Chuang, I. L. Quantum Computation and Quantum Information (Cambridge Univ. Press, 2000).

    MATH  Google Scholar 

  24. Everett, H. III. Relative state formulation of quantum theory. Rev. Mod. Phys. 29, 454–462 (1957).

    ADS  MathSciNet  Article  Google Scholar 

  25. Everett, H. III. The Theory of the Universal Wavefunction, Thesis, Princeton Univ. (1957).

  26. DeWitt, B. S. & Graham, N. (eds) The Many-Worlds Interpretation of Quantum Mechanics (Princeton Univ. Press, 1973).

  27. Landau, L. Das Dämpfungsproblem in der Wellenmechanik. Zeits. Phys. 45, 430–441 (1927).

    ADS  Article  Google Scholar 

  28. von Neumann, J. Mathematical Foundations of Quantum Theory (Princeton Univ. Press, 1955).

    MATH  Google Scholar 

  29. Laplace, P. S. A Philosophical Essay on Probabilities (Dover, 1951).

    MATH  Google Scholar 

  30. Zurek, W. H. Environment-assisted invariance, causality, and probabilities in quantum physics. Phys. Rev. Lett. 90, 120404 (2003).

    ADS  MathSciNet  Article  Google Scholar 

  31. Zurek, W. H. Probabilities from entanglement, Born’s rule from envariance. Phys. Rev. A 71, 052105 (2005).

    ADS  MathSciNet  Article  Google Scholar 

  32. Auletta, G. Foundations and Interpretation of Quantum Theory (World Scientific, 2000).

    Book  Google Scholar 

  33. Gleason, A. M. Measures on closed subspaces of Hilbert space. J. Math. Mech. 6, 855–893 (1957).

    MathSciNet  Google Scholar 

  34. Zurek, W. H. Relative states and the environment: einselection, envariance, quantum Darwinism, and the existential interpretation. Preprint at <> (2007).

  35. Schlosshauer, M. & Fine, A. On Zurek’s derivation of the Born rule. Found. Phys. 35, 197–213 (2005).

    ADS  MathSciNet  Article  Google Scholar 

  36. Barnum, H. No-signalling-based version of Zurek’s derivation of quantum probabilities: A note on ‘Environment-assisted invariance, entanglement, and probabilities in quantum physics’. Preprint at <> (2003).

  37. Wheeler, J. A. in Complexity, Entropy, and the Physics of Information (ed. Zurek, W. H.) 3 (Addison Wesley, 1990).

    Google Scholar 

  38. Darwin, C. On the Origin of Species (John Murray, 1859).

    Google Scholar 

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I am grateful to R. Blume-Kohout, F. Cucchietti, J. P. Paz, D. Poulin, H.-T. Quan and M. Zwolak for stimulating discussions. This research was supported by DoE through an LDRD grant at Los Alamos, and, in part, by the Foundational Questions Institute (FQXi).

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Correspondence to Wojciech Hubert Zurek.

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Zurek, W. Quantum Darwinism. Nature Phys 5, 181–188 (2009).

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