Average entropy of a subsystem.

@article{Page1993AverageEO,
  title={Average entropy of a subsystem.},
  author={Page},
  journal={Physical review letters},
  year={1993},
  volume={71 9},
  pages={
          1291-1294
        }
}
  • Page
  • Published 7 May 1993
  • Mathematics
  • Physical review letters
If a quantum system of Hilbert space dimension mn is in a random pure state, the average entropy of a subsystem of dimension m\ensuremath{\le}n is conjectured to be ${\mathit{S}}_{\mathit{m},\mathit{n}}$= ${\mathit{S}}_{\mathit{k}=\mathit{n}+1}^{\mathit{mn}}$ 1/k-m-1/2n and is shown to be \ensuremath{\simeq}lnm-m/2n for 1\ensuremath{\ll}m\ensuremath{\le}n. Thus there is less than one-half unit of information, on average, in the smaller subsystem of a total system in a random pure state. 
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