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 Sm,n= Smnk=n+1 1/k-m-1/2n and is shown to be ~=lnm-m/2n for 1<<m<=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.
- Publication:
-
Physical Review Letters
- Pub Date:
- August 1993
- DOI:
- 10.1103/PhysRevLett.71.1291
- arXiv:
- arXiv:gr-qc/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
- E-Print:
- 10 pages, LaTeX. Title change and minor corrections added before publication in Phys. Rev. Lett. 71 (1993) 1291. Alberta-Thy-22-93