Average Entropy of a Subsystem

Details Average Entropy of a Subsystem Average Entropy of a Subsystem

1993-05-07

arxiv.org/abs/gr-qc/9305007v2

Phys.Rev.Lett. 71 (1993) 1291-1294

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

10 pages, LaTeX. Title change and minor corrections added before publication in Phys. Rev. Lett. 71 (1993) 1291. Alberta-Thy-2

Scientific paper

10.1103/PhysRevLett.71.1291

If a quantum system of Hilbert space dimension $mn$ is in a random pure state, the average entropy of a subsystem of dimension $m\leq n$ is conjectured to be $S_{m,n}=\sum_{k=n+1}^{mn}\frac{1}{k}-\frac{m-1}{2n}$ and is shown to be $\simeq \ln m - \frac{m}{2n}$ for $1\ll m\leq n$. 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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