Symmetry implies independence

Details Symmetry implies independence Symmetry implies independence

2007-03-08

arxiv.org/abs/quant-ph/0703069v1

Nature Physics 3, 645 - 649 (2007)

Physics

Quantum Physics

LaTeX, contains 4 figures

Scientific paper

10.1038/nphys684

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.

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