Information Security and Cryptography Research Group

Symmetry of large physical systems implies independence of subsystems

Renato Renner

Nature Physics, vol. 3, pp. 645 - 649, Jul 2007, Preliminary version is available at

Given a quantum system consisting of many parts, we show that symmetry of the system's state, i.e., invariance under swappings of the subsystems, implies that almost all of its parts are virtually identical and independent of each other. This result generalises de Finetti's classical representation theorem for infinitely exchangeable sequences of random variables as well as its quantum-mechanical analogue. It has applications in various areas of physics as well as information theory and cryptography. For example, in experimental physics, one typically collects data by running a certain experiment many times, assuming that the individual runs are mutually independent. Our result can be used to justify this assumption.

BibTeX Citation

    author       = {Renato Renner},
    title        = {Symmetry of large physical systems implies independence of subsystems},
    journal      = {Nature Physics},
    pages        = {645 - 649},
    volume       = {3},
    year         = {2007},
    month        = {7},
    note         = {Preliminary version is available at},

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