Average entropy of a subsystem
Abstract
If a quantum system of Hilbert space dimension mn is in a random pure state, the average entropy of a subsystem of dimension m<=n is conjectured to be S_{m,n}= S^{mn}_{k=n+1} 1/km1/2n and is shown to be ~=lnmm/2n for 1<<m<=n. Thus there is less than onehalf unit of information, on average, in the smaller subsystem of a total system in a random pure state.
 Publication:

Physical Review Letters
 Pub Date:
 August 1993
 DOI:
 10.1103/PhysRevLett.71.1291
 arXiv:
 arXiv:grqc/9305007
 Bibcode:
 1993PhRvL..71.1291P
 Keywords:

 05.30.Ch;
 03.65.w;
 05.90.+m;
 Quantum ensemble theory;
 Quantum mechanics;
 Other topics in statistical physics thermodynamics and nonlinear dynamical systems;
 General Relativity and Quantum Cosmology;
 High Energy Physics  Theory
 EPrint:
 10 pages, LaTeX. Title change and minor corrections added before publication in Phys. Rev. Lett. 71 (1993) 1291. AlbertaThy2293