Average entropy of a subsystem

1993/05/31 by Don N. Page · 42 citations
Computer Science · Mathematics · Physics and Astronomy · #Combinatorics #Computability, Logic, AI Algorithms #Dimension (graph theory) #Entropy (arrow of time) #Hilbert space #Mathematical physics #Mathematics #Physics #Quantum Computing Algorithms and Architecture #Quantum many-body systems #Quantum mechanics #gr-qc #hep-th

paper · pdf · doi:10.1103/physrevlett.71.1291

published as Phys.Rev.Lett.71:1291-1294,1993 · 10 pages, LaTeX. Title change and minor corrections added before publication in Phys. Rev. Lett. 71 (1993) 1291. Alberta-Thy-22-93

openalex publication_date 1993/08/30 · arxiv created 1993/08/31 · arxiv updated 2014/11/17 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05

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\ensuremath≤n is conjectured to be S_m,n= S_k=n+1^mn 1/k-m-1/2n and is shown to be \ensuremath≃lnm-m/2n for 1\ensuremath≪m\ensuremath≤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.

Citations

• ON THE FINITE HILBERT TRANSFORMATION

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