Average entropy of a subsystem.

  title={Average entropy of a subsystem.},
  journal={Physical review letters},
  volume={71 9},
  • 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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Mathematical Methods in Physics
Volume II J. S. R. Chisholm and Rosa M. Morris Amsterdam: North-Holland. 1964 Pp. xviii + 717. Price 72s. This book is a valuable addition to an ever-growing collection of mathematical texts written
  • 19, 1028 (1978); cf. E. Lubkin and T. Lubkin, ”Average Quantal Behavior and Thermodynamic Isolation,” University of Wisconsin- Milwaukee preprint WISC-MILW-92-TH-12
  • 1992
Ann. Phys
  • Ann. Phys
  • 1988
Integral Equations and Their Applications to Certain Problems in Mechanics
  • Mathematical Physics and Technology
  • 1957
Black Hole InformationUniversity of Alberta report Alberta- Thy-23-93, hep-th/9305040), to be
  • Proceedings of the 5th Canadian Conference on General Relativity and Relativistic Astrophysics
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Commun. Math. Phys
  • Commun. Math. Phys
  • 1970
Quart. J. Math
  • Quart. J. Math
  • 1951